AP Physics 1-Outline of Topics for 2016-2017

Kinematics-Motion with Constant Acceleration

Final Velocity Under Constant Acceleration

(time dependent) Rearrange from definition of acceleration to produce Kinematics equation I

Example 1-A

A boat is moving at 12 m/s, east. If it slows and ends up going 6.0 m/s, west 6.0 seconds later, find the

acceleration of the boat.

Example 1-B

A rocket ship is moving at 35.0 m/s, to the right of an observer. If it slows and ends up going 15.0 m/s, to the

left of the observer over a time of 5.0 seconds later, find the acceleration of the rocket.

Displacement Under Constant Acceleration Derive from displacement using average velocity and Kinematics equation I to produce

Kinematics equation II

Example 1-C

A car is traveling at a constant speed. A cat walks into the road ahead of the car. The maximum

deceleration the brakes can provide is 3.5 m/s2. If the car comes to a stop 2.35 seconds after the brakes were

applied, what was the original speed of the car?

Example 1-D

If car starts from rest and accelerates at 0.35 m/s2, how far will the car travel over a time interval of 31

seconds?

Example 1-E

How long would it take for a car, moving initially at 5 m/s and with an acceleration of 2.2 m/s2 to travel 112

m?

Final Velocity After Any Displacement Under Constant Acceleration

(time independent) Derive from displacement using average velocity and Kinematics equation I to produce

Kinematics equation III

Example 1-F

A car travels 101 m while accelerating from rest to 88 km/hr (24.4 m/s.) How far will the same car travel if it

speeds up from rest to 100 km/hr?

Example 1-G

A car decelerates from 100 km/hr to 30 km/hr in a time of 27 seconds. How far will the car travel while it

was braking?

Graphical Analysis of Motion Position vs. Time

Speed/Velocity vs. Time

Acceleration vs. Time

Example 1-H

A bug starts from rest and crawls until it reaches its top speed. It then crawls at this speed for a time. It then senses

food and slows down until it reaches the food and stops to eat.

1. Sketch a position vs. time graph for the above situation.

2. Sketch a velocity vs. time graph for the above situation.

Example 1-I

Sketch the conversion of the following position time graph to a velocity vs. time graph.

Example 1-J

For the above Velocity vs. Time graph;

1. Sketch the Position vs Time graph

2. Sketch the Acceleration vs Time graph

Objects in Free Fall (Under Constant Acceleration)

Define Free Fall

What is “g”?

What are the limitations of our investigations and assumptions?

Rework Kinematics Equations I, II, & III for an object in Free Fall.

Example 1-K

A ball is thrown into the air with a speed of 14 m/s. How long does it take to reach its highest elevation?

Example 1-L

A ball is thrown into the air with a speed of 14 m/s. What is the highest elevation it reaches above the point it

was thrown?

Example 1-M

A ball is thrown into the air with a speed of 14 m/s from a point 1.4 m above the ground. What is the balls

speed when it is 1.7 m above the ground?

Example 1-O

A ball is dropped from the edge of a tall cliff.

1. Sketch the Position vs Time graph

2. Sketch the Velocity vs Time graph

Example 1-P

A ball is thrown vertically upward from the edge of a tall cliff.

1. Sketch the Position vs Time graph

2. Sketch the Velocity vs Time graph

Example 1-Q

A ball is thrown vertically downward from the edge of a tall cliff.

1. Sketch the Position vs Time graph

2. Sketch the Velocity vs Time graph

Unit 2: Motion in Two Dimensions Operations with Vectors

I. Vector Addition

1. Graphical Methods

a. Draw to scale

b. Add head to tail

2. Rectangular Resolution.

a. Break into rectangular components

b. Add algebraically

c. Find resulting vector Vector Addition Example 2-A

A tagged caribou is tracked by means of satellite collar. It awakes from where it was tagged and moves 40 km, north. It then

moves 25 km at 30° south of east. Later it moves 30 km due east. Finally the caribou moves 50 km at 60° north of west.

What is the displacement of the caribou?

Vector Addition Example 2-B

A sailor is attempting to sail a course directly northeast at 20 km/hr. There is a current flowing directly south at 5 km/hr. The

wind is blowing at 25 km/hr at 30° north of west. What is the resulting velocity of the sailor?

Vector Addition Example 2-C

The Lockheed SR-71A Blackbird set the record speed for any airplane: 981 m/s. Suppose you observe this plane ascending at

this speed. For 20.0 s, it flies at an angle of 15.0° above the horizontal, then for another 10.0 s its angle of ascent is increased to

35.0°. Calculate the plane’s total gain in altitude, its total horizontal displacement, and its resultant displacement.

Projectile Motion

I. Projectile Launched Horizontally

i. motion in one dimension is independent of motion in another

ii. initial vertical velocity is zero 2 D Kinematics Example 2-D

A rock is thrown horizontally from the top of a 150.0 m cliff. How far out from the bottom of the cliff will the rock land if it is

thrown with a speed of 12 m/s?

2 D Kinematics Example 2-E

A body is found 3.7 m from the base of an apartment complex. The deceased lived on a floor that is 54 m above the ground. Is

it reasonable to assume the fall was accidental?

II. Projectile Launched at an Angle

2 D Kinematics Example 2-F

An arrow is shot at an angle of 60° to the horizontal and hits a target that is 150 m distant. What was the speed of the arrow

when it left the bow?

2 D Kinematics Example 2-G

A baseball is hit from a point 1 meter above the ground. If the ball leaves the bat at 177 km/hr at an angle of 50° and the 3.6 m

high fence is 104 m from home plate, is the hit a home run?

2D Kinematics Graphing Motion-2-H

A rock is thrown at a 45° angle from the top of a very high cliff and allowed to fall to the valley below.

Sketch a position vs. time graph for the above situation.

Sketch a Velocity vs. time graph for the above situation.

Unit 3

Chapter 4: MOTION AND FORCE: DYNAMICS

4.1 Force

- Definition of force

- Free Body Diagrams

4.2 Newton's First Law of Motion

- Contrast Aristotle's and Galileo's views of motion

- Statement of Newton's first law of motion

- Definition of inertia

Example 3-A

A 15 N force is provided by a rope pulling north on a cart while another rope is pulling 10 N, east.

a) Draw the FBD for this problem.

b) Find the net force on the cart by the ropes.

Example 3-B

Four ropes are tied to a crate, each one pulling as follows,

Rope1 = 10 lbs, N

Rope2 = 20 lbs, E

Rope3 = 7 lbs, S

Rope4 = 6 lbs, W

Where would you tie a 5th

rope and how hard would you have to pull to keep the crate at rest? For

ease in calculation you may assume the crate to be mass-less.

4.3 Mass

- Definition of mass and standard units of mass

4.4 Newton's Second Law of Motion

- Statement and equation of Newton's second law of motion

Example 3-C

A box, with a mass of 2.75 kg is sitting on a table. There is a rope tied to the box and you pull on

it, exerting a force of 20.0 N at an angle of 35.0° above the horizontal. A second rope is tied to the

other side of the box, and your friend exerts a horizontal force of 12.0 N. What is the acceleration

of the box?

4.5 Newton's Third Law of Motion

- Statement of Newton's third law of motion

- Examples of this law

4.6 Weight - The Force of Gravity and The Normal Force

- Calculation of weight using the acceleration due to gravity

- Discuss the value of g near the surface of the earth

- Definition and discussion of the normal force

Example 3-D

A 300 kg sign is supported by two cables so that it is positioned between two buildings. One

cable makes a 50° angle to the top of the sign, while the other cable makes a 60° angle to the

top of the sign.

a) Draw the FBD for this problem.

b) Find the tension in each cable.

Example 3-E

A 30 N force is used to throw a 1.5 kg mass into the air.

a) Draw the FBD for this problem.

b) Find the acceleration of the mass.

4.8 Applications Involving Friction & Inclines

- Definition of kinetic friction and its relationship to the normal force between surfaces

- Definition of static friction

- Coefficients of static and kinetic friction

- Normal and frictional forces on an inclined plane

Example 3-F

A worker is attempting to push a 20 kg crate across the floor. When she pushes with 250 N at 30°

to the top of the crate, the crate just starts to move. How strong is the friction force between the

crate and floor?

Example 3-G

A block that weighs 50 N is sitting at rest on an inclined plane of 30°. How strong should the

friction force be to keep the block from sliding down the ramp?

Example 3-H

A 5 kg block is sitting at rest on an inclined plane of 30°. What is the coefficient of static friction

between the block and the ramp?

Example 3-I

A box, with a mass of 9.20 kg is sitting on a ramp that has an incline of 30.0° to the horizontal.

There is a rope tied to the box and you pull on it trying to pull the box up the ramp, exerting a

force of 65 N at an angle of 35.0° above the plane of the ramp. If the box doesn’t move, what is

the coefficient of friction between the box and ramp?

Example 3-J

A box, with a mass of 5.00 kg is placed on a ramp that has an incline of 30.0° to the horizontal.

3.0 seconds after being placed on the ramp, the box is moving at 1.7 m/s. What is the coefficient

of friction between the box and the ramp?

Example 3-K

A block is pushed, from rest, vertically up a wall, a distance of 4.2 m by a 25 N force acting at 30

to the vertical. At this height its speed is 0.75 m/s. If the coefficient of friction between the block

and wall is 0.19, find the mass of the block.

Example 3-L

A box, with a mass of 5.00 kg is sitting on a horizontal surface. There is a rope tied to the box and

you pull on it, exerting a force of 64 N. Another rope connects the first box to a second box which

has a mass of 3.00 kg.

a) What is the acceleration of each box?

b) What is the tension in the rope between the boxes?

Unit 3B

CH 5: CIRCULAR MOTION, GRAVITATION

5.1 Kinematics of Uniform Circular Motion

Definition of uniform circular motion

Derivation of the equation for centripetal acceleration of an object moving in a circle at constant

speed

Example 3B-A

A test car moves at a constant speed around a circular track. If the car is 48.2 m from the track’s center and has a centripetal

acceleration of 8.05 m/s2

, find the tangential speed of the car.

Example 3B-B

A dog is sitting 150 cm from the center of a merry-go-round looking at a cat on the ground beside the merry-go-round. If the

dog revolves for 35 seconds, and sees the cat 5 times, what is the centripetal acceleration of the dog?

5.2 Dynamics of Uniform Circular Motion

Understand that centripetal force is not some new type of force

Understand that centrifugal force does not exist

Example 3B-C

Suppose you are twirling an object tied to a rope in a horizontal circle, but not necessarily in the plane of your hand. If the

tension in the rope is 100 N and the object has a mass of 3.7 kg and the rope is 1.4 m long find:

a) The angle the rope makes to the horizontal.

b) The tangential speed of the object.

Example 3B-D A 2 kg ball is rotated in a vertical circle by a light, rigid stick which has a length of 3 m. The stick is attached to a motor that

keeps the ball moving at a constant speed of 12 m/s.

a) Draw the FBD for the ball at highest and lowest point on the circle.

b) Find the tension in the stick when the ball is at the highest and lowest positions on the circle.

5.3 A Car Rounding a Curve

Driving on a curve examples

Banking angles calculation

Example 3B-E If a roadway is banked the proper angle, a car can round a curve without assistance from friction between tires and the road.

As a result, the speed the car can travel around the curve is increased. Find the appropriate banking angle for a 900.0 kg car,

moving at 20.5 m/s to round a curve of radius 85.0 m.

5.6 Newton's Law of Universal Gravitation

Newton's derivation of his law of universal gravitation

Statement of the law of universal gravitation

Cavendish experiment and the value of the universal gravitation constant

Example 3B-F Find the attractive force between two 1 kg masses that are separated by 1 m.

5.7 Gravity Near the Earth's Surface

Derivation of the acceleration due to gravity at the surface of the earth

Geophysical applications

Example 3B-G An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object

after it has been moved to a distance of 6 R from the center of the planet?

5.8 Satellites and "Weightlessness"

The relationship between the speed and the orbital radius of a satellite

Apparent weightlessness in a satellite and in an elevator

Example 3B-H Suppose an astronaut were to land on a planet that is ¾ the mass of the earth ½ the radius of the earth. What is the value for the

acceleration due to gravity on the surface of this planet?

Unit 4

WORK AND ENERGY

6.1 Work Done by a Constant Force

- Definition of work done by a constant force

Example 4-A

A 10 N force is applied to a crate at angle of 30° to the top of the crate. If the floor is very smooth, how much

work is done in pushing the crate 4 m across the floor?

6.2 Work Done by a Varying Force

- Graphical method of estimating the work done by a varying force

Example 4-B

A force moves an object in the direction of the force as shown in the graph above. Find the work done when the

object moves from 0 to 4.0 m.

6.3 Kinetic Energy and the Work-Energy Theorem

- Definition of energy as the ability to do work

- Definition of kinetic energy and the derivation of its equation

- Statement of the work-energy theorem

6.4 Potential Energy

- Definition of potential energy and gravitational potential energy

- Equation for the change in gravitational potential energy

- General relationship between the change in potential energy and the force

producing that change

- Equation for the change in elastic potential energy

6.5 Conservative and Nonconservative Forces

- Distinguish between conservative and nonconservative forces

- General form of the work-energy theorem

6.6 Mechanical Energy and its Conservation

- Statement of the law of conservation of energy

Example 4-C

Consider a 30 kg child sliding down a very slick hill on a sled. The mass of the sled is 20 kg and the hill is 100 m

long with an incline of 30°. If the child is moving at 2 m/s at the top of the hill, what is her speed at the bottom

of the hill?

Example 4-D

A person pushes a 50.0 kg crate across a floor by applying a constant force of 150.0 N at angle of 30.0° to the

top of the crate. If the coefficient of friction between the crate and the floor is 0.12 and the person pushes the

box 30.0 m across the floor, find;

a) The work done by each force on the crate.

b) The net work done on the crate.

Example 4-E

Suppose the child from example C is on an almost identical hill, except this hill is not as slick. If the child’s

speed at the bottom of the hill is 10 m/s;

a) Find the work done by friction on the child/sled.

b) Find the coefficient of friction.

6.10 Power

- Definition of power

Example 4-F

A car with a mass of 900 kg climbs a 20° incline at a steady speed of 60 km/hr. If the total resistance

forces acting on the car add to 500 N;

a) What is the power output of the car in watts?

b) In horsepower?

Unit 5 CH.7-LINEAR MOMENTUM

7.1 Momentum and its Relation to Force

- Definition of linear momentum

- Restatement of Newton's second law of motion in terms of momentum

7.2 Conservation of Momentum

- Derivation of the conservation of momentum theorem for a one dimensional collision

7.3 Collisions and Impulse

- Definition of impulse

Example 5-A

A 0.15 kg baseball, moving at 30 m/s, is slowed and caught by a catcher who exerts a constant force of 375 N.

a) How long does it take this force to stop the ball?

b) How far does the ball travel before stopping?

Example 5-B

A 5 kg mass is sitting at rest when it has a varying force applied as shown in the graph above.

a) What is the change in momentum of the mass after 26 seconds?

b) What is the velocity of the mass at the end of 26 seconds?

7.4 - 7.6 Conservation of Energy and Momentum in Collisions

- Definition of elastic and inelastic collisions and problems involving both types of collisions

Example 5-C

A car of mass 1000 kg travels east at 30 m/s, and collides with a 3000 kg truck traveling west at 20 m/s.

a) If the collision is completely inelastic, how fast are the car and truck going, and in what direction, after

the collision?

b) What percentage of the kinetic energy is lost in the collision?

c) What happens if the collision is elastic?

Example 5-D

A 2.5 kg mass is allowed to slide down a 2.50 m long frictionless ramp. At the bottom of the ramp it collides with a

4 kg block sitting on a table stopping the 2.5 kg mass. The 4 kg block slides across the 40 cm wide table with a

coefficient of friction of 0.3. The 4 kg block then collides with a 3 kg mass suspended by a 2 m long cord, after

which the 4 kg block stops. If the 3 kg mass swings to maximum angle of 30° to the vertical, find the angle of

inclination of the ramp at the beginning.

7.7 Collisions in Two Dimensions

- Problem solving for collisions in two dimensions

Example 5-E

A 70 kg ice skater is gliding west at 3 m/s. He collides with a 55 kg skater who is moving south at 4 m/s. If they

collide and embrace, what will be their velocity directly after they collide?

Example 5-F

A 3 kg ball is rolling east at 4 m/s. It collides with a 5 kg ball at rest. After colliding the 3 kg ball is rolling at 3.2

m/s at an angle of 30° north of east. What is the velocity of the 5 kg ball after the collision?

Unit 6 (Ch. 16, 18, & 19)

Part I: ELECTRIC CHARGE AND ELECTRIC FIELD

16.1 Static Electricity; Electric Charge and its Conservation

- The origin of the word electricity is described

- Definition of electrostatics and the nature of an electric charge

- State the law of electrostatics and the law of conservation of charge

16.2 Electric Charge in the Atom

16.3 Insulators and Conductors

- Explain the charging an object by contact

- Definition of conductors and insulators

- Understand the distribution of charge in a conductor

- Discuss semiconductors

16.4 Induced Charge: the Electroscope

- Explain the charging of an object by induction

16.5 Coulomb's Law

- State Coulomb's law and its equation to calculate the electrostatic force between two charges

- Define the permittivity of free space

Example 6-A

Four charges are arranged in a square with sides of length 2.5 cm. The two charges in the top

right and bottom left corners are + 3.0 x 10-6

C. The charges in the other two corners are - 3.0 x

10-6

C. What is the net force exerted on the charge in the top right corner by the other three

charges?

Example 6-B

In the Bohr model of the hydrogen atom, an electron (q = e and a mass of 9.1 x 10-31

kg) is in

an orbit of radius 5.3 x 10-11

m. The attraction of the proton for the electron provides the force

needed to hold the electron in orbit.

a) Find the force of attraction between the two particles.

b) Find the speed of the electron.

Example 6-C

Two identical 0.10 g spheres carrying the same charge are suspended by two threads of equal

length. At equilibrium they are 40 cm away from each other and the two threads have an

angular separation of 60°. Find the charge on each sphere.

Part II: Ch. 18-ELECTRIC CURRENTS 18.1 The Battery

- Batteries are a slow but steady source of charge.

- Batteries are two electrodes, usually immersed in a solution.

- Convert chemical potential to electrical energy.

- Known as EMF or electromotive force.

18.2 Electric Current

- The electric current and its unit, the ampere are defined

18.3 Ohm's Law: Resistance and Resistors

- Ohm's law is stated and its equation is given

18.4 Resistivity

- The factors affecting the resistance of a conductor are discussed

Example 6-D

A copper wire has a length of 160 m and a diameter of 1.00 mm. What is the resistance of the wire?

Example 6-E

Using the wire from example 10-A, if the wire is connected to a 1.5 volt battery, how much current is

running through the wire?

18.6 Electric Power

- The equation relating electric power to current and voltage is given

Example 6-F

An electric space heater is connected across a 120 V outlet. The heater dissipates 1.32 kW of power in

the form of electromagnetic radiation and heat. What is the resistance of the heater?

Part III: Ch. 19-DC CIRCUITS

19.1 EMF and Terminal Voltage

- A source of electromotive force is defined

- The internal resistance of a battery is defined

- The equation to calculate the terminal voltage is derived

Example 6-G

A 5.9 Ω resistor is placed across the terminals of a battery with an internal resistance of 0.10 Ω and

provides an emf of 12 V. Find the current flowing across the battery and the terminal voltage of the

battery?

19.2 Resistors in Series and Parallel

- Series and parallel circuits are analyzed and calculations of equivalent resistance, current and

voltage drop are performed

Example 6-H

Three resistors are placed in series and connected to a 10 V battery. If the listed resistance on each is R1=8 ,

R2=8 , and R3=4 ; what is the current flowing through the battery?

Example 6-I

Three resistors are placed in parallel and connected to a 10 V battery. If the listed resistance on each is R1=8 ,

R2=8 , and R3=4 ; what is the current flowing through the battery?

Example 6-J

You have three resistors; a 6 Ω, an 8 Ω, and a 10 Ω. Sketch the arrangement and find the equivalent

resistance of the three when arranged in:

a) Series

b) Parallel

c) The 8 Ω and 10 Ω are in parallel with each other but in series with the 6 Ω.

19.3 Kirchhoff's Rules/Laws

- Kirchhoff's laws to solve complex networks are given

Junction rule

Loop rule Example 6-K

Find the current flowing through the 5 and 9 resistors in the following circuit.

Example 6-L

Find the current flowing through each branch in the following circuit.

Example 6-M

Find the current flowing through each branch in the following circuit.

Example 6-N

Find the current flowing through each branch in the following circuit.

Unit 7-(Ch. 11, 12)

Simple Harmonic Motion

11.1 Simple Harmonic Motion

Oscillation is defined

Period, amplitude, and frequency defined.

11.2 Energy in a Simple Harmonic Oscillator

Example 7-A

An object of mass, m, is at the end of a spring that vibrates with a frequency of 0.88 Hz. When an

additional 680 g mass is added to the object, the frequency of vibration is 0.60 Hz. What is the mass, m,

of the object?

Example 7-B

A 13000 N car starts from rest and rolls down a hill from a height of 10.0 m. It then moves across a level

surface and collides with a light spring-loaded guardrail.

a) Neglecting any losses due to friction and assuming the spring has a spring constant value of 1.0 x 106 N/m,

find the maximum distance the spring is compressed.

b) Calculate the maximum acceleration of the car after contact with the spring.

c) If the spring is compressed by only 0.30 m, find the energy lost through friction.

11.3 Simple Harmonic Motion, Period, and Sinusoidal Nature

Oscillation is defined

Period, amplitude, and frequency defined.

Example 7-C Find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the

equation for its position as a function of time is

X = (.250 m)

11.4 The Simple Pendulum

The factors relating to the period are examined.

The small angle approximation is emphasized.

Example 7-D

Suppose a grandfather clock of length, l, runs “on time” on the earth. If the same clock were taken to the

moon which has 1/6 the mass of the earth, what would the new length of the pendulum on the clock be if

it were to still run correctly? Express your answer as a percentage of l.

11.5 Damped Harmonic Motion

Underdamped, Overdamped, and Critically damped situations are discussed.

Waves 11.6 Forced Vibrations; Resonance

Students should understand the inverse-square law, so they can calculate the intensity of waves at a given

distance from a source of specified power and compare the intensities at different distances from the source.

11.7 Wave Motion

Sketch or identify graphs that represent traveling waves and determine the amplitude, wavelength, and

frequency of a wave from such a graph.

Apply the relation among wavelength, frequency, and velocity for a wave.

Example 7-E:

A Golden Retriever sits watching waves in a pond. He measures the time for crests to pass as 3.0

seconds. If he estimates the distance between crests as 6.5 m, what is the calculated speed of the

waves?

Example 7-F:

A 2.4 m length of wire has a mass of 9.1 g. What is the speed of transverse waves along the wire

when a 2.27 kg weight is hung from one end?

11.8 Types of Waves Students should understand the difference between transverse and longitudinal waves, and be able to

explain qualitatively why transverse waves can exhibit polarization.

11.9 Energy Transported by Waves

Understand qualitatively the Doppler effect for sound in order to explain why there is a frequency shift in both

the moving-source and moving-observer case.

11.10* Intensity Related to Amplitude and Frequency

11.11 Reflection and Transmission

Describe reflection of a wave from the fixed or free end of a string.

11.12 Interference; Principle of Superposition

Students should understand the principle of superposition, so they can apply it to traveling waves moving in

opposite directions, and describe how a standing wave may be formed by superposition.

11.13 Standing Waves: Resonance

Sketch possible standing wave modes for a stretched string that is fixed at both ends, and determine the

amplitude, wavelength, and frequency of such standing waves.

Example 7-G:

A particular string has a length of 63.0 cm and a mass of 30 g. If the tension in the string has a tension of

87.0 N:

a) What is the fundamental frequency of the string?

b) What is the frequency of the fifth harmonic?

Sound 12.1 Characteristics of Sound

Speed of Sound

12.2 Intensity and Sound Level (Relative) Intensity

Students should understand the inverse-square law, so they can calculate the intensity of waves at a given

distance from a source of specified power and compare the intensities at different distances from the source.

Example 7-H:

One day the sound level intensity in a powerhouse is measured when only four of the 7 turbines are in

operation and the reading was 115 dB. If you returned another day and all seven turbines were

operating, what would sound level reading be on the day all turbines were operating?

12.4 Sources of Sound: Vibrating Strings and Air Columns

Strings

Tubes (open at both ends)

Tubes (closed at one end)

Describe qualitatively what factors determine the speed of waves on a string and the speed of sound.

Describe possible standing sound waves in a pipe that has either open or closed ends, and determine the

wavelength and frequency of such standing waves.

Example 7-I:

A tube, open at one end, has an overall length of 25.0 cm. The temperature is 20°C.

a) What is the fundamental frequency?

b) What is the frequency of the fifth harmonic?

12.6 Interference of Sound Waves; Beats

12.7 Doppler Effect

Understand qualitatively the Doppler effect for sound in order to explain why there is a frequency shift in both

the moving-source and moving-observer case.

Unit 8

Part I-Center of Mass and Angular Motion 7.10 Center of Mass (gravity)

8.1 Angular Quantities

- angular displacement

- angular velocity

- angular acceleration

- relation between linear and angular quantities

Example 8-A

Express 28° in radian measure.

Example 8-B

A mass tied to the end of string 90 cm long is allowed to swing through a 15 cm long arc. Find the angle the string

swings with respect to the vertical;

a) in radians

b) in degrees

Example 8-C

A fan turns at 900 rpm

a) Find the angular speed of any point on one of the fan blades.

b) Find the tangential speed of the tip of the blade if the distance from the center to the tip is 20 cm.

Example 8-D

The spin-drier of a washing machine revolving at 900 rpm slows down uniformly to 300 rpm while making 50

revolutions. ;

a) Find the angular acceleration.

b) Find the time required to revolve through the 50 revolutions.

8.2 Motion under Constant Angular Acceleration

- Linear vs. Angular kinematics

Example 8-E

A wheel rotates with constant angular acceleration of 3.50 rad/s2. If the angular speed of the wheel is 2.00 rad/s at

t = 0;

a) Through what angle does the wheel rotate between t = 0 and t = 2.00 s? Express in both radians and

revolutions.

b) What is the angular speed of the wheel at 2.00 s?

Example 8-F

An airplane propeller slows from an initial angular speed of 12.5 rev/s to a final speed of 5.00 rev/s. During this

process the propeller rotates through 21.0 revolutions. Find the angular acceleration of the propeller in rad/s2

assuming it’s constant?

Example 8-G

A CD rotates from rest up to an angular speed of 31.4 rad/s in a time of 0.892 s.

a) What is the angular acceleration of the disc, assuming the acceleration is constant?

b) Through what angle does the disc turn while coming up to speed?

c) If the radius of the disc is 4.45 cm, find the final tangential speed of a microbe riding at the rim of the disc?

d) What is the magnitude of the tangential acceleration of the microbe at that time?

Part II-Torque and Rotational Inertia 8.4 Torque

Torque, moments, and arms: defined.

9.1 Statics and Conditions for Equilibrium

9.2 Solving Statics Problems

Use of FBD’s and the equilibrium of torque and forces is described.

Example 8-H

A uniform 1.4 kg rod is hinged on one end and supported by a rope attached to the opposite end of the

rod. The angle between the rope and rod is 34°. (a) What is the tension in the rope?

(b) What are the two components of the support force exerted by the hinge?

Example 8-I

Jessica is sitting on one end of a 4.5 m long see-saw. Ralph is on the other side. If Jessica and Ralph’s

masses are 44 kg and 52 kg respectively, how far is Ralph from the center of the see-saw if the two are

balanced?

8.5 Rotational Dynamics

Moments of Inertia

Second Law for Rotation

Torque and Angular Rotation

Example 8-J

A baseball player loosening up his arm before a game tosses a 0.150 kg baseball, using only the rotation

of his forearm to accelerate the ball. The forearm has a mass of 1.50 kg and length of 0.350 m. The ball

starts at rest and released with a speed of 30.0 m/s in 0.300 seconds. (a) Find the angular acceleration of the arm-ball.

(b) Find the moment of inertia of the system consisting of the forearm and ball.

(c) Find the torque exerted on the system that results in the angular acceleration found in part (a).

Example 8-K

A solid, frictionless cylindrical reel of mass M = 3.00 kg and radius, R = 0.400 m is used to draw water

from a well. A bucket of mass m = 2.00 kg is attached to a cord that is wrapped around the cylinder. (a) Find the tension in the cord and acceleration of the bucket.

(b) If the bucket starts from rest at the top of the well and falls for 3.00 seconds before hitting the water, how far

does it fall?

Part III-Rotational Kinetic Energy and Angular Momentum 8.7 Rotational Kinetic Energy

Rotational Kinetic Energy: defined

As a part of Conservation of Mechanical Energy

Work-Energy Theorem application

Example 8-L

A ball of mass M and radius R starts from rest at a height of 2.00 m and rolls down a 30.0° slope. What is

the linear speed of the ball as it leaves the incline? You may assume the ball rolls without slipping.

Example 8-M

A 5.00 kg block on a table is attached by a string strung over a pulley to second mass of 7.00 kg hanging

from the string. The pulley has a mass of 2.00 kg and is a hollow cylinder with a radius 0.050 m and

spins on a frictionless pulley. If the coefficient of friction between the table and block is 0.350, find the

speed of the system when the hanging block has dropped 2 m.

8.8 Angular Momentum

Angular Momentum: defined

Second Law for Rotation in terms of Angular Momentum

Conservation of Angular Momentum

Example 8-N

A student, holding two dumbbell weights sits on a lab stool that is free to rotate around a vertical axis

with negligible friction. The moment of inertia of the student, weights, and stool is 2.25 kg∙m2. The

student is set in rotation with arms outstretched, makes one complete revolution in 1.26 seconds. (a) What is the initial angular speed of the system?

(b) As she rotates, the student pulls the weights inward so that the new moment of inertia of the system is 1.80

kg∙m2. What is the new angular speed of the system?

(c) Find the work done by the student on the system while she was pulling the weights in. You may ignore the

energy lost through dissipation in her muscles.

Example 8-O

A merry-go-round modeled as a disk of mass 1.00 x 102 kg and radius 2.00 m is rotating in horizontal

plane about a frictionless vertical axle. (a) After a 60.0 kg student jumps onto the merry-go-round, the system’s angular speed falls to 2.00 rad/s. If the

student walks slowly from the edge toward the center, find the angular speed of the system when he reaches a point

0.500 m from the center.

(b) Find the change in the system’s rotational kinetic energy caused by his motion toward the center.

(c) Find the work done on the student as he walks to the point 0.500 from the center.