Circular motion

Day 1, 10/29/2013

Rotating – turning around an internal axis

RevolvingTurning about an external axis

Linear speed, vHow far you go in a certain amount of timeMiles per hour, meters per second

Rotational (angular) speed, ώHow many times you go around in a certain

amount of timeRevolutions per minute, rotations per hour,

radians per second

Which horse has a larger linear speed on a merry go round, one on the outside or one on the inside?

Outside.

Which horse has a greater rotational speed?Neither, all the horses complete the circle in the same amount of time.

Tutorial on Circular motionhttp://www.youtube.com/watch?v=nb4VzvfkSN0

The number of revolutions per second is called the frequency, f. Units are Hertz, Hz.

The time it takes to go all the way around once is called the period, T. Units could be seconds, minutes, hours, years.

Frequency is related to period by f = 1 / T

What is the frequency of Earth’s rotation on its axis?Period, T = 24 hours = 86400 secondsf = 1 / Tf = 1 / 86400f = 1.16 x 10-5 Hz

RememberVelocity = distance / time

For circular motion, the distance traveled is all around the circle… the circumference.

The circumference = 2prSo…

v = 2pr / T

Solve this!

A disk with a radius of 0.25 m turns at 33 revolutions in one minute. What is the speed of a point along the outer edge?

r = 0.25 mf = 33 rev/min X

= 0.55 rev/sec or Hz v = ?

v = 2pr / TCould it be that v = 2pr(f)?v = 2p (0.25)(0.55)v = 0.864 m/s

Uniform Circular Motion, UCM: moving in a circle with a constant speed.

Question: Is there a constant velocity when an object moves in a circle with a constant speed?

No, the direction changes, therefore the velocity changes.

If the velocity changed, the object is actually ACCELERATING even while moving at the same speed.