Question

A pulley of radius 1.5 m is rotated about its axis by a force F = (12t - 3t2) N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5 kg m2, the number of rotations made by the pulley before its direction of motion is reversed, will be K/π. The value of K is ________.

Answer 1

The correct answer is 18

Fig.

I = 4.5 kg m2
$FR=Iα$
$α=\frac{(12t–3t^2)×1.5}{4.5}=4t−t^2$
$w=∫αdt=2t^2–\frac{t^3}{3}$
w=0
$⇒t^2(2–\frac{t}{3})0$
t=6 sec
$θ=∫_{0}^{6}[2^t2–\frac{t^3}{3}]dt=[\frac{2t^3}{3}–\frac{t^4}{12}]_{0}^{6}$
$=[\frac{2}{3}×6^3–\frac{6^4}{12}]=36$
$n=\frac{36}{2π}$
$=\frac{18}{π}$