A ballet dancer has a maximum net torque of 45 Nm, and the moment of inertia of his body is 30 kg mA2. if he starts twirling from rest and keeps accelerating for 95 seconds, how fast will he be rotating? a) b) if he holds rocks in his hands, which variables in this problem would change, in which direction, and why?

(a) 142.5 rad/s

Explanation:

Torque = 45 Nm

Moment of inertia = 30 kgm^2

w0 = 0, t = 95 second

(a) Let it is rotating with angular speed w.

Torque = moment of inertia x angular acceleration

45 = 30 x α

α = 1.5 rad/s^2

Use first equation of motion for rotational motion

w = w0 + α t

w = 0 + 1.5 x 95

w = 142.5 rad/s

(b) if he hold rocks, then the moment of inertia change and then angular acceleration change and then final angular velocity change.