Question

a 4kg uniform rod is fixed to rotate around its midpoint. the rod accelerated from rest by a torque of magnitude 20 N * m for 10s through what angle does the rod rotate over time

Answer 1

We know that, torque is given by:

Tau = F x R = F x L/2 = m a L/2

Tau = m (L/2 alpha) L/2 = m L^2/4 alpha

alpha = tau x 4/m L^2

alpha = 20 x 4/4 L^2 = 20/L^2

We know from eqn of motion that,

theta = wt + 1/2 alpha t^2

theta = 0 + 1/2 x 20/L^2 x 10^2 = 1000/L^2

We need value of L that is the length of rod to find an "L" independent value of theta.

Hence, theta = 1000/L^2