First slide

Rotational motion

Question

The moment of inertia of a body about a given axis is 1.2 kg-m². Initially, given axis the body is at rest. In order to produce a rotational kinetic energy of 1500 J and angular acceleration of 25 rads^-2 a torque that must be applied about that axis for a duration of

Moderate

A

4 s
B

2 s
C

8 s
D

10 s

Solution

As, $I = 1 .2 kg \cdot m^{2}, E_{r} = 1500 J, α = 25 {rads}^{- 2}, ω_{1} = 0, t = ?$
$\begin{array}{l} Now, E_{r} = \frac{1}{2} {Iω}^{2} \\ \Rightarrow ω = \sqrt{\frac{2 E_{r}}{I}} \\ = \sqrt{\frac{2 \times 1500}{1 .2}} = 50 {rads}^{- 1} \\ From ω_{2} = ω_{1} + αt \\ 50 = 0 + 25 t \\ \Rightarrow t = 2 s \end{array}$

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