5/26/2018 5 Uniform Circular Motion

1/15

Chapter 5

Dynam ics of Uni formCircu lar Mot ion

5/26/2018 5 Uniform Circular Motion

2/15

Uniform Circular Mot ion

DEFINITION OF UNIFORM CIRCULAR MOTION

Uniform circular motion is the motion of an object

traveling at a constant speed on a circular path.

vr

T

2

Let Tbe the time it takes for the object to

travel once around the circle.

5/26/2018 5 Uniform Circular Motion

3/15

Centr ipetal A ccelerat ion

The direction of the centripetal acceleration is towards the

center of the circle; in the same direction as the change in

velocity.

rva

c

2

5/26/2018 5 Uniform Circular Motion

4/15

Centr ipetal A ccelerat ion

Example: The Effect of Radius on Centripetal Acceleration

The bobsled track contains turns

with radii of 33 m and 24 m.Find the centripetal acceleration

at each turn for a speed of

34 m/s. Express answers as

multiples of .sm8.9 2

g

gac 6.3

gac 9.4

5/26/2018 5 Uniform Circular Motion

5/15

Centr ipetal Force

The centripetal force is the name given to the net force

required to keep an object moving on a circular path.

The direction of the centripetal force always points toward

the center of the circle and continually changes direction

as the object moves.

rvmmaF cc

2

5/26/2018 5 Uniform Circular Motion

6/15

Centr ipetal Force

The Effect of Speed on Centripetal Force

5/26/2018 5 Uniform Circular Motion

7/15

Centr ipetal Force

A Trapeze Act

In a circus, a man hangs upside down from a trapeze, legs

bent over and arms downward, holding his partner. Is it harderfor the man to hold his partner when the partner hangs

straight down and is stationary or when the partner is swinging

through the straight-down position?

5/26/2018 5 Uniform Circular Motion

8/15

Satel l i tes in Circular Orbits

There is only one speed that a satellite can have if the

satellite is to remain in an orbit with a fixed radius.

5/26/2018 5 Uniform Circular Motion

9/15

Satel l i tes in Circular Orbits

Global Positioning System

5/26/2018 5 Uniform Circular Motion

10/15

Satel l i tes in Circular Orbits

5/26/2018 5 Uniform Circular Motion

11/15

Apparent Weight lessn ess and A rt i f ic ia l Gravity

Apparent Weightlessness and Free Fall

In each case, what is the weight recorded by the scale?

5/26/2018 5 Uniform Circular Motion

12/15

Apparent Weight lessn ess and A rt i f ic ia l Gravity

Artificial Gravity

At what speed must the surface of the space station move

so that the astronaut experiences a push on his feet equal to

his weight on earth? The radius is 1700 m.

5/26/2018 5 Uniform Circular Motion

13/15

Samp le problems for uni form circu lar mo t ion

Example 1 A car has a lateralaccelerationof0.87g. This represents the maximum

centripetal acceleration that can be attained

without skidding out of the circular path. If acar is travelling at a constant 40m/s, what is

the minimum radius of curve it can

negotiate?

Answer: R=190m

5/26/2018 5 Uniform Circular Motion

14/15

Samp le problems for uni form circu lar mo t ion

Example 2 In a carnival ride, the passengerstravel at a constant speed in a circle of

radius 5.0m. They make one complete circle

in 4.0s. What is their acceleration?

Answer: arad=12m/s2

5/26/2018 5 Uniform Circular Motion

15/15

Samp le problems for uni form circu lar mo t ion

Example 3 A sled with a mass of 25.0kg rests on a horizontalsheet of frictionless ice. It is attached by a 5.00-m rope to a

post set in the ice. Once given a push, the sled revolves

uniformly in a circle around the post. If a sled makes one

complete revolution in 12.0s, find the force F exerted on it

by the cord.

Answer: F=34.3 N