Circular Motion

Kinematics of Uniform Circular Motion(Description of Uniform Circular Motion)

Dynamics of Uniform Circular Motion(Why does a particle move in a circle?)

Reading Question

Reviewing for the exam I have spent

1. Zero hours2. ½ hour3. 1 hour4. 1 ½ hours5. 2 hours6. 2 ½ hours7. 3 or more hours

Reading Question

1. x- and y-axes. 2. x-, y-, and z-axes.3. x- and z-axes.4. r-, t-, and z-axes.

Circular motion is best analyzed in a coordinate system with

Reading Question

1. x- and y-axes. 2. x-, y-, and z-axes.3. x- and z-axes.4. r-, t-, and z-axes.

Circular motion is best analyzed in a coordinate system with

Reading Question

1. the circular weight.2. the angular velocity.3. the circular velocity.4. the centripetal acceleration.

The quantity with the symbol w is called

Reading Question

1. the circular weight.2. the angular velocity.3. the circular velocity.4. the centripetal acceleration.

The quantity with the symbol w is called

Reading Question

1. points toward the center of the circle.2. points toward the outside of the circle.3. is tangent to the circle.4. is zero.

For uniform circular motion, the net force

Reading Question

1. points toward the center of the circle.2. points toward the outside of the circle.3. is tangent to the circle.4. is zero.

For uniform circular motion, the net force

Circular Motion

Uniform circular motion is a particle moving at constant speed in a circle.

Circular Motion

Is the velocity changing?

Yes, changing in direction but not in magnitude.

Is the speed changing?

The period is defined as the time to make one complete revolution

T

rv

2

period

cecircuferen

Circular Motion

The angle q is the angular position.

How do we describe the position of the particle?

Again q is defined to be positive in the counter-clock-wise direction.

r

sradians )(

Angles are usually measured in radians.

s is arc length.

r is the radius of the circle.

Circular MotionRadians

For a full circle.

r

sradians )(

rad22

r

r

r

sfullcircle

rad23601 0 rev

rad2

360rad1rad1

0

rs

Circular MotionAngular velocity

The angular displacement is

if

if

if

ttt

Average angular velocity

dt

d

tt

0

limit

Instantaneous angular velocityWe will worry about the direction later.

Like one dimensional motion +- will do. Positive angular velocity is counter-clock=wise.

Circular MotionCoordinate System

Circular MotionSo, is there an acceleration?

Circular MotionSo, is there an acceleration?

Student Workbook

Student Workbook

Student Workbook

Student Workbook

bankF

w

T a

Student Workbook

engineF

w

dragliftF ,

side of plane

w

bankF

liftF

Which way is the plane turning?

To the left

Circular Motion

So, is there an acceleration? Yes

rv

a2

directed toward the center of curvature (center of circle)

Class QuestionsA particle moves cw around a circle at constant speed for 2.0 s. It then reverses direction and moves ccw at half the original speed until it has traveled through the same angle. Which is the particle’s angle-versus-time graph?

1. 2. 3. 4.

Class QuestionsA particle moves cw around a circle at constant speed for 2.0 s. It then reverses direction and moves ccw at half the original speed until it has traveled through the same angle. Which is the particle’s angle-versus-time graph?

1. 2. 3. 4.

Class Questions

1. (ar)b > (ar)e > (ar)a > (ar)d > (ar)c

2. (ar)b = (ar)e > (ar)a = (ar)c > (ar)d

3. (ar)b > (ar)a = (ar)c = (ar)e > (ar)d

4. (ar)b > (ar)a = (ar)a > (ar)e > (ar)d

5. (ar)b > (ar)e > (ar)a = (ar)c > (ar)d

Rank in order, from largest to smallest, the centripetal accelerations (ar)ato (ar)e of particles a to e.

1. 2. 3. 4. 5.

Class Questions

1. (ar)b > (ar)e > (ar)a > (ar)d > (ar)c

2. (ar)b = (ar)e > (ar)a = (ar)c > (ar)d

3. (ar)b > (ar)a = (ar)c = (ar)e > (ar)d

4. (ar)b > (ar)a = (ar)a > (ar)e > (ar)d

5. (ar)b > (ar)e > (ar)a = (ar)c > (ar)d

Rank in order, from largest to smallest, the centripetal accelerations (ar)ato (ar)e of particles a to e.

1. 2. 3. 4. 5.

Circular Motion

Circular MotionPROBLEM-SOLVING STRATEGY 7.1 Circular motion problems

MODEL Make simplifying assumptions.

VISUALIZE Pictorial representation. Establish a coordinate system with the r-axis pointing toward the center of the circle. Show important points in the motion on a sketch. Define symbols and identify what the problem is trying to find.

Physical representation. Identify the forces and show them on a free-body diagram.

SOLVE Newton’s second law is

. Determine the force components from the free-body diagram. Be careful with signs.

. SOLVE for the acceleration, then use kinematics to find velocities and positions.

ASSESS Check that your result has the correct units, is reasonable, and answers the questions.