The M.I. of a body about the given axis is $1.2 ext{ kg m}^2$. Initially, the body is at rest. In order to h

Question

The M.I. of a body about the given axis is $1.2 	ext{ kg m}^2$. Initially, the body is at rest. In order to have a rotational kinetic energy of 1500 J, an angular acceleration of $25 	ext{ rad/s}^2$ must be applied about that axis for a duration of:

Accepted Answer

Given:
Initial angular velocity, $\omega_0 = 0$
Moment of inertia, $I = 1.2 	ext{ kg m}^2$
Rotational kinetic energy, $K = 1500 	ext{ J}$
Angular acceleration, $\alpha = 25 	ext{ rad/s}^2$

The rotational kinetic energy is given by:
$$K = \frac{1}{2} I \omega^2$$
$$1500 = \frac{1}{2} 	imes 1.2 	imes \omega^2$$
$$1500 = 0.6 \omega^2$$
$$\omega^2 = \frac{1500}{0.6} = 2500$$
$$\omega = 50 	ext{ rad/s}$$

Using the kinematic equation for rotational motion:
$$\omega = \omega_0 + \alpha t$$
$$50 = 0 + 25 	imes t$$
$$t = \frac{50}{25} = 2 	ext{ s}$$

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