A hamster running in a wheel of radius 13 cm spins the wheel at 13 revolutions per minute.

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

Let

r = 13 cm be the radius of the wheel,

ω = 13 revolutions / minute be angular velocity,

v (to be computed) be linear velocity.

a)

To convert ω to radians/sec we use the folowing identities:

revolution = 2π radians

minute = 60 sec

Subbstitute:

ω = 13 revolutions / minute = 13 × 2π radians / 60 sec = 0.433 π radians/sec = 1.36 radians/sec

b)

Linear velocity is given by the formula

v = ωr

provided ω is in radians/sec

Substitute actual numbers

v = 1.36 × 13 = 17.7 cm/sec