circular motion.ppt

7/27/2019 Circular Motion.ppt

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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?)


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Reading Question

Reviewing for the exam I have spent1. Zero hours

2. hour

3. 1 hour

4. 1 hours5. 2 hours

6. 2 hours

7. 3 or more hours


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Reading Question

1. x- andy-axes.

2. x-,y-, andz-axes.

3. x- andz-axes.

4. r-, t-, and z-axes.

Circular motion is best analyzed in a coordinate system with


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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


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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


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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


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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


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Circular Motion

Uniform circular motion is a particle moving at constant

speed in a circle.


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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


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Circular Motion

The angle q is the

angular position.

How do we describe theposition of the particle?

Again q is defined to be

positive in the counter-clock-

wise direction.

r

sradians )(q

Angles are usually measured in

radians.

s is arc length.

r is the radius of the circle.


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Circular Motion

Radians

For a full circle.

r

sradians )(q

rad22

q r

r

r

sfullcircle

rad23601 0 rev

rad2

360rad1rad1

0

qrs


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Circular Motion

Angular velocity

The angular displacement is

if qqq

if

if

ttt

qqqww

Average angular velocity

dt

d

tt

qqw

0

limit

Instantaneous angular velocity We will worry about the directionlater.

Like one dimensional motion +-

will do. Positive angular velocity

is counter-clock=wise.


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Circular MotionCoordinate System


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Circular MotionSo, is there an acceleration?


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Circular MotionSo, is there an acceleration?


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Student Workbook


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Student Workbook


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Student Workbook


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Student Workbook

bankF

w

T a


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Student Workbook

engineF

w

dragliftF

,

side of plane

w

bankF

liftF

Which way is the plane turning?

To the left


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Circular Motion

So, is there an acceleration? Yes

r

va

2

directed toward the

center of curvature

(center of circle)


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Class QuestionsA particle moves cw around a circle at constant speed for

2.0 s. It then reverses direction and moves ccw at half theoriginal speed until it has traveled through the same angle.

Which is the particles angle-versus-time graph?

1. 2. 3. 4.


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Class QuestionsA particle moves cw around a circle at constant speed for

2.0 s. It then reverses direction and moves ccw at half theoriginal speed until it has traveled through the same angle.

Which is the particles angle-versus-time graph?

1. 2. 3. 4.


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Class Questions

1. (ar)b > (ar)e > (ar)a > (ar)d > (ar)c2. (ar)b = (ar)e > (ar)a = (ar)c > (ar)d3. (ar)b > (ar)a = (ar)c = (ar)e > (ar)d4. (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.


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Class Questions

1. (ar)b

> (ar)

e> (a

r)

a> (a

r)

d> (a

r)

c

2. (ar)b = (ar)e > (ar)a = (ar)c > (ar)d3. (ar)b > (ar)a = (ar)c = (ar)e > (ar)d4. (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.


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Circular Motion


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Circular Motion

PROBLEM-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 Newtons 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.

circular motion.ppt

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