Question

A grind stone starts from rest and has a constant angular acceleration of 4.0 rad/sec². The angular displacement and angular velocity, after 4 sec. will respectively be

• A. 32 rad, 16 rad/sec
• B. 16 rad, 32 rad/sec
• C. 64 rad, 32 rad/sec
• D. 32 rad, 64 rad/sec

Answer 1

Answer: (A)

32 rad, 16 rad/sec

Answer 2

$\omega_{1} = 0,\alpha = 4rad/\sec^{2},t = 4sec$

Angular displacement $\theta = \omega_{1}t + \frac{1}{2}\alpha t^{2} = 0 + \frac{1}{2}4(4)^{2} = 32rad.$

∴ Final angular $\omega_{2} = \omega_{1} + \alpha t = 0 + 4 \times 4 = 16rad/sec$