June 16, 2014

Angular and Linear Velocity

Part 2

• All points on the same rotating object have the same angular velocity.

• If two rotating objects are connected so that they rotate as a single object, such as different parts on a wheel of a bicycle or a record on a record player, then they have the same angular velocity.

June 16, 2014

• If two rotating objects are connected by their rims, then their rims have the same linear velocity.

1. The propellers on an average freighter have a radius of 4 feet. At full speed ahead, the propellers turn at 150 revolutions per minute.

a) What is the angular velocity, in radians per minute, at the tip of the blade? At the center of the propeller?

b) What is the linear velocity, in feet per minute, at the tip of the blades? At the center of the propeller?

June 16, 2014

2. Jack and Jill are riding on a Ferris wheel. Jack observes that it takes 20 seconds to make a complete revolution.

Their seat is 25 feet from the axle of the wheel.

A. What is the angular velocity in revolutions

per minute? Degrees per minute?

Radians per minute?

B. What is their linear velocity?

3. A small gear, with a radius of 5 cm, is turning with an angular velocity of 20 radians per second

It drives a larger gear of radius 15 cm.

A. What is the angular velocity of the

teeth on the large gear?

B. What is the linear velocity of the teeth on the large gear?

C. What is the angular velocity of a point at the center of the large gear?

June 16, 2014

4. Two pulleys, one with radius of 2 inches and another with a radius of 8 inches, are connected by a belt (see figure). If the 2 inch pulley is caused to rotate 3 revolutions per minute, determine the revolutions per minute of the 8 in pulley.

5. At the Cable Car Museum you can see the four cable lines that are used to pull car cables up and down the hills of San Francisco. Each cable car travels 9.55 miles per hour, caused by a rotating wheel whose diameter is 8.5 feet. How fast is the wheel rotating? Express your answer in revolutions per minute.

June 16, 2014

practice: pg. 130,131 #3,5,13,15,27-35odd, 37, 39

homework: pg. 130,131 #4,6,14,16,28-36 even, 38, 41