• Why don’t riders of a roller coaster fall out at the top of a loop? … Does the speed of the coaster have anything to do with it?

• If a cup of water is swung in a circle, why doesn’t the water fall out? Does speed matter here?

• When a car travels fast around a curve in a road, why does a passenger get “thrown” towards the far side of the car?

• If you do this in a golf cart with no door, what will happen to the passenger?

Animations:

“Car” with No Door

“Car” with Door

In each of the previous examples, there was a force present that caused the object to travel in a circle.

• Without the force, the object in motion continues along a straight-line path.

• With the force, the object in motion is pulled or pushed towards the ___________________. This force is then appropriately called a _____________ force, which means “center-seeking”.

center of the circle centripetal

Centripetal vs. Centrifugal ForceIf an object traveling in a circle experiences a force towards the center (centripetal), why then do we feel like there is a force throwing us away from the center when we travel in a circular path?

We know that feeling is simply due to _______, the tendency to continue in motion in a _____________.

However, sometimes the term __________ “force”, which means ______________, is used to describe this, but it’s actually ____________

inertiastraight line

centrifugalcenter-fleeingNOT A FORCE!!

Centripetal AccelerationIf an object traveling in a circle experiences a centripetal force, then it must experience a centripetal ___________ as well.

But… if an object is traveling in a circle at constant speed, how can it be accelerating?

Recall that acceleration is the rate at which _______ changes.. The ________ of the velocity vector is continually changing!

acceleration

velocitydirection

cma

Centripetal Force Equation

Newton’s 2nd Law can then be used to find an expression for the centripetal force that causes the centripetal acceleration:

OR

cF

cFR

mv2

Linear Speed (or Velocity) Equation

How can we calculate the linear speed, v, of an object traveling in a circle at a constant speed?

t

dvspeed v

Where…

• _____ = circumference

• T = _______, the time for 1 revolution

Recall that the direction of the velocity vector is _______ to the circular path.

T

R2

R2Period

tangent

Example Problem: Linear Speed and Rotational SpeedCalculate the linear speed, v, of a bug riding on the edge of an old 8 cm radius record that is rotating at a rotational speed of 45 rpm.

1st find the period, T, in units of sec/rev:

sec75.0

60

min1

min45

rev

sx

rev

revreciprocalT

sec3.1

2nd, find the speed, v:

• If the bug moved halfway in to R = 4 cm, find the new linear speed. The rotational speed will be __________, so the period, T, doesn’t change.

•As the bug moves to the center, it’s linear speed will approach ______!

•To summarize, if the rotational speed (rpm’s) is constant, as R ↑, linear speed, v __

scm

s

cmv 38

3.1

)8(2

scm

s

cmv 19

3.1

)4(2

the same

zero

↑

If you didn’t follow

Calvin’s dad the 1st time, do

you now??

An Application: Train WheelsIn order to travel around a curve, a train’s outside wheels must travel faster than it’s inside wheels, (for the same reason that the starting points are staggered in a race. If they weren’t staggered, the runners on the outside would run a longer distance!) But, if the train wheels are connected to the same axle, how can they do that?

Train wheels are slightly _________, and the tracks are slightly rounded so that only a small part of the wheel is actually in contact with the track at any time!

A view of the tapered wheels… looking down the track

Picture from Paul Hewitt’s Conceptual Physics

tapered

When a train makes a right turn, the tendency of the train to go straight (Newton’s 1st Law of Inertia!) “forces” the larger-diameter part of the left wheel on the left track and the smaller-diameter part of the right wheel on the right track. In 1 revolution of the axle, then, the left wheel will travel a larger distance, and thus, travels faster!

The Swings Ride at an Amusement Park

FBD: The centripetal force on a swing/rider is the _________ component of the ________.

T

W =mg Why do the swings move farther out as the speed goes up?

Fc

horizontaltension

A car going around a flat curve

In order for a car to be able to go around a flat curve, ________ must supply the necessary centripetal force. If there is NOT enough ________, then the car will skid!

friction

friction

Ff

W

N

Equations:

= = AND =(Static or Sliding?)

fFcF fFRmv2 NIF NO SKID!

4. A car going around a banked curve

In addition to friction, we bank curves to make it easier to “make” the curve.

The __________ component of the normal force is towards the _______ of the circle, and thus significantly contributes to the centripetal force.

W

Fc

horizontal center

Satellite Physics – Circular Orbits

Illustration from Isaac Newton, Philosophiae Naturalis Principia Mathematica, Book III

Isaac Newton was the first to argue that if a projectile is given enough velocity, it would fall _______ the earth rather than into it!! The projectile is then called a ________ and the trajectory is called an ______.

around

satellite

orbit

So, what is the ONLY force acting on a satellite (planets, moons or man-made)?

The _____________ force between the satellite and planet it’s orbiting (which would equal the ______ of the satellite at that point).

If the orbit is a circular orbit, then, the

gravitational force is the ___________ force. (Note that the direction of the gravitational force on the satellite is always towards the center of the planet - it’s “center-seeking”!)

gravitational

weight

centripetal

But, wait…. If the force of gravity (or weight) is the only force acting on a satellite, why do astronauts experience what is known as “weightlessness” (they appear to be floating!) when in orbit?

Actually they are ______________!! Gravity is ________ there (or they wouldn’t stay in orbit!). They and the space shuttle are BOTH ______. It would be more accurate to say: They are experiencing “____________________” or “__________ weightlessness”!

NOT weightless

falling

normalforcelessness

NOT zero

apparent

So, if gravity is the ONLY force acting on the satellite, why doesn’t the satellite “fall” and hit the earth?

Remember that it ________.... In order for a satellite to be moving in a circular orbit, it must be traveling at just the right ______ to ___________ ___________

IS falling!

velocity

fall aroundthe earth

We can calculate the required velocity, v, for a satellite’s circular orbit:

Earth

V (NOT a force)

R

WFc mg

R

mv

2

gRv 2

gRvsat

W

R = radius of orbit (distance from center of earth)

Mass of satellite __________ and thus has _______________ on the required speed! Why does that make sense?

cancelsno influence

The “Rotor” Amusement Park Ride:

The “rotor” is spun in a circle at a high speed. At top speed, the floor is dropped, leaving the riders “stuck” to the wall! How does this work??

So, the _____________ is the centripetal force, and ________ is the force that keeps the person from sliding down.

Ff,static

Normal

mg

Normal Forcefriction

What forces act on the rider and in what direction do they act? Which FBD is correct?

Futuristic Space Stations:

One of the problems with people living long-term in an orbiting space station is the zero “apparent gravity” environment.

One potential solution to this problem is to spin the orbiting space station about its central axis in order to simulate gravity. The centripetal force on a person in this situation is a _______ force. Top

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