Pre Calc B
6.1 Day 3 – Linear/Angular Speed

Name______________________________
Solverson
Linear Speed v  r
t
***When possible, give me an exact answer and an answer rounded to the nearest hundredth.
Arc Length
s  r
Angular Speed

Here are the facts we talked about in class:
1. All points on the same rotating object have the same angular speed.
2. 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 speed.
3. If two rotating objects are connected by their rims, then their rims have the same linear speed.
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 speed, in radians per minute, at the tip of the blades?
At the center of the propeller?
B. What is the linear speed, in feet per minute, at the tip of the blades?
At the center of the propeller?
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 speed in revolutions per minute?
Degrees per minute?
Radians per minute?
B. What is their linear speed in feet per minute?
3.
A small gear, with a radius of 5 cm, is turning with an angular speed of 20 radians per second
It drives a larger gear of radius 15 cm.
A.
What is the linear speed of the teeth on the large gear?
B. What is the angular speed of the teeth on the large gear?
C. What is the angular speed of a point at the center of the large gear?
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.