Question

A disc is rotating with an angular velocity w₀. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes (w₀/2) after n rotations. How many more rotations will it make before coming to rest?

• A. n
• B. 2n
• C. n/2
• D. n/3

Answer 1

Answer: (D)

n/3

Answer 2

From third equation, w² = w₀² – 2aq ]

Ž (w₀/2)² = w₀² – 2a(2np)

Ž 4pna = 3/4 w₀² ……(1)

Let no. of rotations before coming to rest = n¢

Ž 0 =$\left( \frac{\omega_{0}}{2} \right)^{2}$– 2a (2pn¢) Ž 4pn¢ a = $\frac{\omega_{0}^{2}}{4}$ ….(2)

from (1)/(2) n/n¢ = 3 Ž n¢ = n/3