1.

A cylinder of mass 5 kg and radius 30 cm,is free to rotate about its axis;it receives an angular impulse of 3 kg square metre per seconds,initally followed by a similar impulse after every 4 s .What is the angular speed of the cylinder after 30s of the initial impulse?

Answer»

It is given that,
mass of CYLINDER, m = 5kg
radius of cylinder , r = 30CM = 0.3 m
ANGULAR IMPULSE , ∆L = 3kgm²/s

here, initial angular speed is \omega_0=0
angular speed after 4s = \omega

we know,
angular impulse = change in angular momentum
3 = I(\omega-\omega_0)
Here I is moment of inertia.
3 =1/2 mr²(\omega -0)
6 = 5 × (0.3)² × \omega
\omega = 40/3 rad/s

now, use \omega=\omega_0+\alpha t
40/3 = 0 + \alpha × 4
\alpha = 10/3 rad/s

now angular speed after 30 sec = 0 + 10/3 × 30
= 300/3 = 100 rad/s


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