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Rotational Mechanics — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsRotational Mechanics3 Marks
Question
A body rotating at 20rad/s is acted upon by a constant torque providing it a deceleration of 2rad/s2. At what time will the body have kinetic energy same as the initial value if the torque continues to act?
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Answer

Initial angular velocity = 20rad/s

Therefore $\alpha=2\text{rad/s}^2$

$\Rightarrow\text{t}_1=\frac{\omega_2}{\alpha_1}=\frac{20}{2}=10\text{sec}$

Therefore 10sec it will come to rest.

Since the same torque is continues to act on the body it will produce same angular acceleration and since the initial kinetic energy = the kinetic energy at a instant.

So initial angular velocity = angular velocity at that instant

Therefore time require to come to that angular velocity,

$\Rightarrow\text{t}_2=\frac{\omega}{\alpha_2}=\frac{20}{2}=10\text{sec}$

therefore time required = t1 + t2 = 20sec.

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