Question

A flywheel whose moment of inertia about its axis of rotation is 16kg-m^(2) is rotating freely in its own plane about a smooth axis through its centre. Its angular velocity is 9rads^(-1) when a torque is applied to bring it to rest in t_(0) seconds find t_(0) if (a). The torque is constant and of magnitude 4N-m (b). The magnitude of the torque after t second is given by kt.

Answer 1

Given: Moment of Inertia = 16kg m²

Angular velocity = 9 rads

To Find: The torque and the magnitude of torque.

Solution:

a) Angular impulse  = Change in angular momentum  

Therefore, t0=Iω  

t0 = Iω/τ

= 16 × 9/5

= 36

b) ∫rdt = Iω

∫kdt = Iω

= kt²/2 = Iω

= t0 = √Iω√2/k

= √ 16 × 9 √2/k

= 12√2/k

Answer: The magnitude of torque is 12 √2/k