A hamster running in a wheel of radius 11 cm spins the wheel one revolution in 12 seconds.

Question

A hamster running in a wheel of radius 11 cm spins the wheel one revolution in 12 seconds.

a) 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 velocity = ω = 2 × π × f

where f is the frequency of rotation. In this case, f = 1 revolution / 12 seconds.

2×π = 1 revolution, so

ω = [ (2×π) / 1 revolution] × ( 1 revolution / 12 seconds)

ω = 2 π radians per 12 seconds

ω = (2/12) π radians / second = (1/6) π radians per second

b) linear velocity v = ω × r = [ (1/6) π radians per second ] × 11 cm = (11/6) × π cm / second.

Answer 2

a) 2π / 12

b) 22π / 12