Question

(ii) A cylinder of mass 5 kg and radius 30cm and free to rotate
about its axis ,receives an angular impulse of 3 kg-m/s;
initially followed by a similar impulse after every 4sec .What
is the angular speed of the cylinder 30sec after the initial
impulse? The cylinder is initially at rest.​

Answer 1

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=0ω

0

=0

angular speed after 4s = \omegaω

we know,

angular impulse = change in angular momentum

3 = I(\omega-\omega_0)I(ω−ω

0

)

Here I is moment of inertia.

3 =1/2 mr²(\omegaω -0)

6 = 5 × (0.3)² × \omegaω

\omegaω = 40/3 rad/s

now, use \omega=\omega_0+\alpha tω=ω

0

+αt

40/3 = 0 + \alphaα × 4

\alphaα = 10/3 rad/s

now angular speed after 30 sec = 0 + 10/3 × 30

= 300/3 = 100 rad/s