Question

A body is in pure rotational motion about an axis. Its angular acceleration is given by: a = 2t. What is the angular distance covered by the body from t=2s to t=3s? It starts from rest at t=0.

(a) 19/3 rad

(b) 0 rad

(c) 2/3 rad

(d) 5/3 rad

I have been asked this question in exam.

This intriguing question comes from Kinematics of Rotational Motion about a Fixed Axis in portion System of Particles and Rotational Motion of Physics – Class 11

Answer 1

Correct choice is (a) 19/3 rad

For explanation: Let w be the angular velocity & a be the angular acceleration.                                                      Given: dw/dt = a = 2t.                                                                                                                                                              On integrating both sides, we get:

w = t^2  (no integration constant because w=0 at t=0).

Now, dθ/dt = w = t^2

∴ θ = t^3/3.

To find angular distance covered from t=2 to t=3, we can subtract distance covered in 2s from distance covered in 3s.

∴ θ covered = 3^3/3 – 2^3/3                                                                                                                                                        = 19/3 rad.