Ahoop of mass 2 kg, radius 0.5 m is rotating about its center with an angular speed of 3 rad's. a force of 10n is applied tangentially at the rim (a) determine the rotational kinetic energy oh the hoop (b) what is instantaneous change rate of the kinetic energy?

The rotational kinetic energy of the hoop and the instantaneous change rate of the kinetic energy are 2.25 J and 15 J.

Explanation:

Given that,

Mass = 2 kg

Radius = 0.5 m

Angular speed = 3 rad/s

Force = 10 N

(I). We need to calculate the rotational kinetic energy

Using formula of kinetic energy

(II). We need to calculate the instantaneous change rate of the kinetic energy

Using formula of kinetic energy

On differentiating

....(I)

Using newton's second law

Put the value of a in equation (I)

Hence, The rotational kinetic energy of the hoop and the instantaneous change rate of the kinetic energy are 2.25 J and 15 J.

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