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 para

llel to

the velocit

y

Is dire

cted to

wards t

he ...

is la

rger f

or a la

rger 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 position

d tangular velocity

t dtd t

angular accelerationt dt

Circular Motion

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

( )( )

( )( )

x displacement

x dx tv t velocity

t dtv dv t

a 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 r

v r

UCM cont

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

thens r

v r

a r

Uniform Circular Motion

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

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

22v

rr

Uniform Circular Motion

Slide 6-13

Newton’s Second Law

• Net force must point towards center of circle

2

, toward center of circleNET

mvF ma

r

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

motionB. Toward the center of the circle

Checking Understanding

Slide 6-11

Problems due today

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