math 127 Trigonometry

Question

A hamster running in a wheel of radius 10 cm spins the wheel at 39 revolutions per minute.

Give exact answers, using ππ for each question

.a) What is the angular velocity of the wheel? (in radians/sec)   

b) At what linear velocity is the hamster running? (in cm/sec) 

Answer 1

a) Angular speed, ω , is given as 39 revolutions/min. We simply need to convert units to radians (rads) per

second (sec)

1rev = 2π rads

1min = 60secs

39revs/min X 1min/60sec X 2πrads/rev = 78πrads/60sec--->ω = 1.3π rads/sec

b)Linear velocity, v, equals the radius times angular velocity:

v = rω

v = (10cm) X (1.3πrads/sec)

v = 13π cm/sec

Hope this helps!