Chapter 8 - Rotational Motion

Circular Motion

Trip to the Carnival…You and your two friends decide to go ride the merry-go-round. Your one friend says she wants to sit on an outside horse because it moves faster. Your other friend wants to sit on the inside because he says it doesn’t matter where you sit – all the horses are connected so they are all going the same speed.

Who do you agree with???

So many speeds…• Linear Speed

– What we’ve been calling speed up to this point; distance in meters per unit of time

• Tangential Speed– The speed of something moving in a circular path– Called tangential because the direction of motion is

always tangent to the circle

*For circular motion, the terms *For circular motion, the terms linear speedlinear speed and and tangential speedtangential speed can be used interchangeably* can be used interchangeably*

An object will always fly off tangent to it’s circular path…

So many speeds…• Are tangential speeds the same for each point of a

rotating object?• Ex: Bike Wheel

– Inner point and outer points have the same amount of time to travel to very different distances

• Conclusion…– DIFFERENT!!!

Which horse has the greatest tangential speed?OUTTER MOST HORSE

So many speeds…• Rotational Speed

– Refers to the number of revolutions or rotations per unit of time

– Also called Angular Speed– All parts of a rotating object share the same rate of

rotation– Commonly expressed in revolutions per minute or RPM

• Relationship– Tangential speed is directly proportional to both rotational

speed and radial distance.

Which horse has the greatest rotational speed?ALL THE SAME

Example #1

On a rotating platform, if you sit halfway between the rotating axis and the outer edge and have a rotational speed of 20 RPM and a tangential speed of 2 m/s, what will be the rotational and tangential speeds of your friend who sits on the outer edge?

Example #2

A lady bug sits halfway between the axis and the edge of a phonograph record. What will happen to its tangential speed if the RPM rate is doubled? At this doubled rate, what will happen to its tangential speed if it crawls out to the edge?

…so dizzy

…

Review Questions1. Why is the linear speed greater for a horse on the outside

of a merry-go-round than for a horse closer to the center?

2. How are tangential speed and rotational speed related? If the rotational speed of a platform is doubled, how does tangential speed anywhere on the platform change?

3. Consider a bicycle that has wheels with a circumference of 2 m. What is the linear speed of the bicycle when the wheels rotate at 1 revolution per second?