Circular Motion Kinematics of Uniform Circular Motion (Description of Uniform Circular Motion) Dynamics of Uniform Circular Motion (Why does a particle

Circular MotionCircular Motion

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

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

Reading QuestionReading 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


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


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


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

The quantity with the symbol is called


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

The quantity with the symbol is called


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


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


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


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


The angle is the angular position.

How do we describe the position of the particle?

Again 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 MotionCircular MotionRadians

For a full circle.

r

sradians )(

rad22

r

r

r

sfullcircle

rad23601 0 rev

rad2

360rad1rad1

0

rs

Circular MotionCircular 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 MotionCircular MotionCoordinate System

Circular MotionCircular MotionSo, is there an acceleration?

Circular MotionCircular MotionSo, is there an acceleration?

Student WorkbookStudent Workbook




bankF

w

T a


engineF

w

dragliftF ,

side of plane

w

bankF

liftF

Which way is the plane turning?

To the left


So, is there an acceleration? Yes

rv

a2

directed toward the center of curvature (center of circle)

Class QuestionsClass 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 QuestionsClass 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 QuestionsClass 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 QuestionsClass 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 MotionCircular MotionPROBLEM-SOLVING STRATEGY 7.1 PROBLEM-SOLVING STRATEGY 7.1 Circular motion problemsCircular motion problems

MODEL Make simplifying assumptions.MODEL Make simplifying assumptions.

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

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

SOLVE Newton’s second law isSOLVE Newton’s second law is

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

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

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

Documents

Circular Motion Kinematics of Uniform Circular Motion (Description of Uniform Circular Motion) Dynamics of Uniform Circular Motion (Why does a particle