First slide

Torque

Question

A disc can rotate about an axis passing through its centre and perpendicular to the plane of the disc. Initially the disc is stationary and its moment of inertia about the axis is 4 Kg-m². A torque is applied on the disc which varies with time according to the graph shown in figure. Then angular velocity of the disc at the end of 6th second is

Moderate

A

12 rad/s
B

8 rad/s
C

10 rad/s
D

5 rad/s

Solution

Change in angular momentum $= \int_{0}^{t} τ d t = Area under τ -t graph$
$\begin{array}{l} ∴ L - O = \frac{1}{2} \times 2 \times 4 + 4 \times (6 - 2) \Rightarrow L = 20 Joule - S \\ ∴ ω = \frac{L}{I} = \frac{20}{4} rad / s = 5 rad / s \end{array}$

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