Question

A wheel whose moment of inertia is $24kg{m}^2$ starts from rest. Net torque acting on wheel $\tau$ varies with respect to time as shown in the graph. Find the work done by torque in the first 6 seconds.

• A. 6.75 J
• B. 3.75 J
• C. 4.25 J
• D. 9.75 J

Answer 1

The correct option is A 6.75 J

$K.E=\frac{L^2}{2I}$
Area bounded by $\tau -t=$ change in L
$\frac{1}{2}\times 12\times 4-\frac{1}{2}\times 6\times 2=L_f-L_i$
$24-6$ $=L-0$
$L=18$
$K.E=\frac{L^2}{2\times I}=\frac{18\times 18}{2\times 24}=\frac{27}{4}=6.75$
Work done $\Delta K.E=K.E_f-K{F}_i=6.75-0=6.75J$