First slide

Rotational motion

Question

Three children are sitting on a see-saw in such a way that it balances. A 20 kg and a 30 kg boy are on opposite sides at a distance of 2m from the pivot. It the third boy jumps off, thereby destroying balance, then the initial angular acceleration of the board is: (Neglect weight of board)

Easy

A

$0.01 {rads}^{- 2}$
B

$1.0 {rads}^{- 2}$
C

$10 {rads}^{- 2}$
D

$100 {rads}^{- 2}$

Solution

$Net torque, τ = 30 g \times 2 - 20 g \times 2 = 20 g$
$\begin{array}{l} I = 30 \times 2^{2} + 20 \times 2^{2} = 120 + 80 = 200 {kgm}^{2} \\ α = \frac{τ}{I} = \frac{20 g}{200} = \frac{g}{10} = \frac{10}{10} = 1.0 {rads}^{- 2} \end{array}$

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