1

Ch 5. Dynamics of Uniform Circular MotionUniform circular motion constant speed & circular path.

T = time to travel once around the circle.

vr

T

2

Example 1: A Tire-Balancing Machine

The wheel of a car has a radius of 0.29m and it being rotated at 830 revolutions per minute on a tire-balancing machine. Determine the speed at which the outer edge of the wheel is moving.

minsrevolution830

1

s 072.0min 102.1 3 T

sm25s 072.0m 0.2922

Trv

revolutionmin102.1 3

2

5.2 Centripetal Acceleration

9090

speed is constant, but velocity is not

rtv

vv

rv

tv 2

rvac

2

direction of centripetal

acceleration = towards

center of circle

3

Example 3: Effect of Radius on Centripetal AccelerationThe 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 2g

rvac2

gac 6.3sm35m 33

sm34 22

gac 9.4sm48m 24sm34 2

2

4

5.3 Centripetal Force

rvmmaF cc

2

Centripetal Acceleration rvac

2 Centripetal Force

Example 5: The Effect of Speed on Centripetal Force

The model airplane has a mass of 0.90 kg and moves at constant speed on a circle that is parallel to the ground. Find the tension in the 17 mguideline for a speed of 19 m/s.

rvmTFc

2

N 19m 17sm19kg 90.0

2

T

5

5.4 Banked CurvesUnbanked curve static friction centripetal force

Frictionless banked curve centripetal force = horizontal component of the normal force. vertical component of the normal force balances the car’s weight r

vmFF Nc

2

sin

mgFN cos

rgv2

tan ]2[]1[

6

5.4 Banked Curves

Example 8: The Daytona 500

The turns at a Speedway have a radius of 316 m and are banked at 31 degrees. The turns were frictionless. At what speed would the cars have to travel around them?

rgv2

tan tanrgv

31tansm8.9m 316 2v

mph 96 sm43

5.5 Satellites in Circular Orbitssatellite only one speed fixed radius orbit

rvm

rmMGF E

c

2

2

rGMv E

7

5.5 Satellites in Circular Orbits

Example 9: Orbital Speed of the Hubble Space Telescope

Determine speed of Hubble Telescope orbiting at 598 km above earth surface

m10598m1038.6

kg1098.5kgmN1067.636

242211

v

Tr

rGMv E 2

EGMrT

232

Orbital Period of satellite

hmi16900 sm1056.7 3

Global Positioning System

hours 24T

hours 24T

8

5.6 Apparent Weightlessness and Artificial Gravity

Example 13: Artificial Gravity

At what speed must the surface of the space station moveso that the astronaut experiences a push on his feet equal to his weight on earth? The radius is 1700 m.

mgrvmFc

2

2sm80.9m 1700

rgv

9

5.7 Vertical Circular Motion

rvmmgFN

21

1

rvmmgFN

23

3

rvmFN

24

4 rvmFN

22

2