Question

The average net torque Justin exerts on a discus about its axis of spin is 100 Nm during a throw. The mass of the discus is 2 kg, and its radius of gyration about the spin axis is 12 cm. If the discus is not spinning at the start of Justin's throwing action, and the throwing action lasts for 0.20 s, how fast is the discus spinning when Justin releases it?

The answer is 694 rad/s

Please show work/explain steps, Thanks!

Answer 1

from mass = 2kg
and radius of gyration = 12cm = 0.12m
we can find the moment of inertia I = m*Rgyration^2 = 0.0288 kgm^2
now we need to use newton's second law -> torque = I * alpha (alpha - angular acceleration)

so
100 = 0.48 * alpha
alpha = 3472.22 rad/sec^2

the angular velocity is given by:
w = alpha * t
so we have
w = 694.4 rad/sec