Subject: linear speed, linear velocity, angular speed
Name: Lynn
Who are you: Student

A belt has a linear speed of 32 mph. It is spinning three pulleys.
Pulley A has diameter 14 in. radius = 7 inches
Pulley B has diameter 26 in. radius = 13 inches
Pulley C has radius 3 ft. radius = 36 inches

Angular speed in Radians per min for
I got
Pulley A= .08 rads/min Pulley B= .04 rads/min Pulley C=.01 rads/min

How many cm would pulley C travel in 14 seconds?

since I was given linear speed instead of velocity how does that affect the results? Just not sure of the relationship
Lynn

Hi Lynn,

When I looked at your numbers my immediate reaction was that they can't be correct. For example you say that pulley A spins at 0.08 rads/min. There are 2 radians in one revolution and is approximately 3 so there are approximately 6 rads/revolution.

(6 rads/revolution) / (0.08 rads/min) = 75 min/revolution

When the belt is moving at 32 miles per hour the pulley can't take 75 minutes to make one revolution.

The belt is moving at 32 mph. There are 5280 feet in a mile, 12 inches in a foot and 60 minutes in an hour so

32 miles/hour = ^{(32 x 5280 x 12)}/₆₀ = 33792 inches/minute

Pulley A has a radius of 7 inches and hence a circumference of 14 inches. One revolution of the pulley is 2 radians and hence on the circumference of the pulley there are 7 inches/radian.

Thus the pulley is spinning at the rate of

 ³³⁷⁹²/₇ = 4827 radians/minute.

Penny