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 Justins throwing action, and the throwing action lasts for 0.20 s, how fast is the discus spinning when Justin releases it?

Answer 1

Average net torque exerted by Justin on the discus = T = 100 Nm

Mass of the discus = M = 2 kg

Radius of gyration of the discus = k = 12 cm = 0.12 m

Moment of inertia of the discus = I

I = Mk²

I = (2)(0.12)²

I = 0.0288 kg.m²

Angular acceleration of the discus =

I = T

(0.0288) = 100

= 3472.22 rad/s²

Initial angular speed of the discus = ₁ = 0 rad/s

Final angular speed of the discus = ₂

Time period = t = 0.2 sec

₂ = ₁ + t

₂ = 0 + (3472.22)(0.2)

₂ = 694.44 rad/s

The discus is spinning at 694.44 rad/s when Justin releases it.