First slide

Dynamics of rotational motion about fixed axis

Question

A solid disc of mass 2 kg and radius 50 cm can rotate about an axis through its centre O and perpendicular to the plane of the disc. Forces are applied at points A, B and C as shown in figure. Then angular acceleration of the disc is

Moderate

A

2.5 rad/s²
B

5 rad/s²
C

10 rad/s²
D

20 rad/s²

Solution

$τ =$ Net torque about the centre
$\begin{array}{l} = (10 \sin 30^{o} \times 0 .5 + 10 \times 0 .5 - 5 \times 0 .5) N - m \\ \Rightarrow τ = 5 N - m \\ I = \frac{1}{2} \times 2 \times {(0 .5)}^{2} Kg - m^{2} = 0 .25 Kg - m^{2} \\ ∴ α = \frac{τ}{I} = \frac{5}{0 .25} rad / s^{2} = 20 rad / \sec^{2} \end{array}$

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