What is the torque required to achieve this feat?

Question

Suppose David puts a 0.40 kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 110 rpm after 5.0 s. What is the torque required to achieve this feat?
__________ N·m

Answer 1

Torque = (rate of change in angular momentum)
= (change in angular momentum) / time
= ΔL / t

For a mass at the end of a (weightless) sling, the angular momentum L is given by:
L = ωmr²

where:
ω = angular velocity in radians per second.
m = mass of rock
r = length of sling

Putting it all together:

Torque = ωmr² / t

They give you m, r and t in the problem. ω can be computed from knowing 100 rpm, if you keep in mind that 1 revolution = 2π radians.