Section 10 – Rotational Motion

Section 10.1

Uniform Circular Motion

Circular Speed

Period and Frequency

An axis is the straight line around which rotation takes place.

When an object turns about an internal axis—that is, an axis

located within the body of the object—the motion is called

rotation.

When an object turns about an external axis, the motion is

called revolution.

Rotation vs. Revolution

The Ferris wheel turns about an axis.

The Ferris wheel rotates, while the riders

revolve about its axis.

Rotation vs. Revolution

Earth undergoes both types of rotational motion.

• It rotates around an axis passing through its geographical

poles once every 24 hours.

• It revolves around the sun once every 365 ¼ days.

Rotation vs. Revolution

Uniform Circular Motion

Uniform Circular Motion (UCM)

Uniform Circular Motion

Uniform circular motion is the motion of an object traveling

at a constant speed on a circular path.

Circular Speed

If an object travels at constant speed, that constant speed can

be found by taking the distance traveled and dividing by the

associated time of travel. ( v = d / t ).

Lets take a closer look at the components that make up speed:

distance “d” and time ”t”

Circular Speed: Distance

If the time that is used to calculate the constant speed is the

period, or time to complete one circular path, then the correct

distance to use would be the circumference of the circular path.

distance = circumference = 2pr

Circular Speed: Time

There is a special time of travel that is of interest when the

motion of an object repeats itself – This is called the Period.

• Period (T)

The time interval it takes an object to go around a circle

one time.

Circular Speed: Time

Units:

Seconds, minutes, hours, laps, revolutions, etc

(seconds per 1 cycle)

Circular Speed

To determine the constant speed of an object traveling in a

circular path in terms of the time (period) required for the object

to complete one circular path.

Hence, circumference divided by time is the speed of the object:

v =d

t=

2pr

Tr

Example #1

A girl drives her car clockwise around a circular track of radius

30 meters. She completes 10 laps around the track in 2 minutes.

Find her circular speed in m/s.

15.71 m/s

Example #2

A NASCAR driver, traveling at a constant speed, completes a lap

around a circular track of diameter 320 meters in 36 seconds.

What is the circular speed of the car?

27.93 m/s

Example #3

A boy and a girl sit on a merry-go-round with a period of 3.5

seconds. The boy and girl sit 0.75 m and 0.35 m from the center

of the merry-go-round, respectively.

a. Who will be traveling faster? (Boy, Girl, Same?)

b. Calculate the circular speed of each child.

a.) Boy

b.) VB = 1.35 m/s

VG = 0.628 m/s

Frequency

Frequency (f)

The number of revolutions per second or the # of times an object

goes around a circle in 1 second.

Units:

Note: the SI unit of frequency is inverse seconds, or 1/s.

Hertz (Hz)

cycles / sec (cycles per 1 second)

Period vs. Frequency Formulas

T =1

ff =

1

T

Circular Speed expressed with period (T) or frequency (f)

v =2pr

T

v 2rf

Example #4

Hamlet the hamster runs on his exercise wheel, which turns

every 0.5 seconds. What is the frequency?

2 Hz

Example #5

A sock, that is stuck on the inside of the clothes dryer, spins

around the drum once every 2 seconds at a distance of 50 cm

from the center of the drum. What is the socks circular speed?

1.57 m/s

Example #6

What is the radius of an automobile that turns with a frequency

of 11 hertz and has a circular speed of 20 m/s?

0.289 m

Example #7

The wheel of a car has a radius of 0.29 meters and it being rotated at

13.83 hertz on a tire-balancing machine. Determine the speed at which

the wheel is moving.

25.2 m/s

Example #8

A toy car completes 5 laps of its circular track in 1 min 30 seconds.

If the diameter of the track is 2 meters, find:

a. The car’s period

b. The toy car’s frequency

a.) 18 seconds

b.) 0.0556 Hz