Question

A wheel with moment of inertia 25 kg. m2 and angular velocity 10 rad/s begins to speed up, with angular acceleration 15 rad/sec2 . a) After 2 seconds of acceleration, how many radians of rotation has the wheel completed? b) After 3 seconds of acceleration, what is the wheel’s kinetic energy due to rotation?

Answer 1

(A) Angular speed 40 rad/sec

Rotation = 50 rad

(b) 37812.5 J

Step-by-step explanation:

We have given moment of inertia of the wheel
`I=25kgm^2`

Initial angular velocity of the wheel
`\omega _0=10rad/sec`

Angular acceleration
`\alpha =15rad/sec^2`

(a) We know that
`\omega =\omega _0+\alpha t`

We have given t = 2 sec

So
`\omega =10+15*  2=40rad/sec`

Now
`\Theta =\omega _0t+(1)/(2)\alpha t^2=10* 2+(1)/(2)* 15* 2^2=50rad`

(b) After 3 sec
`\omega =10+15* 3=55rad/sec`

We know that kinetic energy is given by
`Ke=(1)/(2)I\omega ^2=(1)/(2)* 25* 55^2=37812.5J`