Lecture 16Friday, October 3

Chapter 6:Circular Motion

Review Example

Macie pulls a 40 kg rolling trunk by a strap angled at 30° from the horizontal. She pulls with a force of 40 N, and there is a 30 N rolling friction force acting on trunk. What is the trunk’s acceleration?

Slide 5-17

For uniform circular motion, the acceleration

Is paralle

l to th

e velocity

Is dire

cted to

wards the ...

is lar

ger for a

larger o

rbit...

33% 33%33%1. Is parallel to the velocity

2. Is directed towards the center of the circle

3. is larger for a larger orbit at the same speed

Problem, interacting bodies

Glider on a air track

Massless, frictionless pulley

m1

m2

Special Assignment

• Special assignment to be handed in Monday: Workbook pages 4-5 and 4-6, exercises 17-22 and page 5-5, exercises 13-15.

• The kinematics of uniform circular motion

• The dynamics of uniform circular motion

• Circular orbits of satellites

• Newton’s law of gravity

Chapter 6Circular Motion, Orbits and Gravity

Topics:

Sample question:The motorcyclist in the “Globe of Death” rides in a vertical loop upside down over the top of a spherical cage. There is a minimum speed at which he can ride this loop. How slow can he go?

Slide 6-1

Uniform Circular Motion

• Uniform magnitude of velocity (speed) is constant

( )( )

( )

t angular positiond tangular velocity

t dtd tangular acceleration

t dt

Circular Motion

• Note similarity to the equations for one-dimensional linear motion

( )( )

( )( )

x displacementx dx tv t velocityt dt

v dv ta t accelerationt dt

• Going from angular velocity to angular displacement:

1 where is frequency (rad/s)

2 rad for uniform circular motion

f i t

T period ff

T

UCM continued

• Travelling at constant speed v around circle• Period is time one around circle = T

2vT rv r

UCM cont

• s is distance travelled around circumference and the definition of the radian tell us

thens rv ra r

Uniform Circular Motion

• Uniform magnitude of velocity (speed) ω, is constant

• But α is not zero because direction of velocity is changing.

22v r

r

Uniform Circular Motion

Slide 6-13

Newton’s Second Law

• Net force must point towards center of circle

2

, toward center of circleNETmvF mar

Example

A level curve on a country road has a radius of 150 m. What is the maximum speed at which this curve can be safely negotiated on a rainy day when the coefficient of friction between the tires on a car and the road is 0.40?

Slide 6-24

Top View

• v

sf

When a ball on the end of a string is swung in a vertical circle:What is the direction of the acceleration of the ball?

A. Tangent to the circle, in the direction of the ball’s motion

B. Toward the center of the circle

Checking Understanding

Slide 6-11

Problems due today

• 5: 24, 25, 29, 30, 31, 35, 36, 37, 39