A time-dependent torque given by τ=a+b sin c t is applied to...

A time-dependent torque given by $\tau=a+b$ sin $c t$ is applied to an object that's initially stationary but is free to rotate. Here $a, b$ and $c$ are constants. Find an expression for the object's angular momentum as a function of time, assuming the torque is first applied at $t=0$.

Angular Momentum At the instant the displacement of a 2.00 $\mathrm{kg}$ object relative to the origin is $\vec{d}=(2.00 \mathrm{m}) \hat{\mathrm{i}}+(4.00 \mathrm{m}) \hat{\mathrm{j}}-(3.00 \mathrm{m}) \hat{\mathrm{k}}$ , its velocity is $\vec{v}=-(6.00 \mathrm{m} / \mathrm{s}) \hat{\mathrm{i}}+(3.00 \mathrm{m} / \mathrm{s}) \hat{\mathrm{j}}+(3.00 \mathrm{m} / \mathrm{s}) \hat{\mathrm{k}}$ and it is subject to a force $\vec{F}=(6.00 \mathrm{N}) \hat{\mathrm{i}}-(8.00 \mathrm{N}) \hat{\mathrm{j}}+(4.00 \mathrm{N}) \hat{\mathrm{k}} .$ Find $(\mathrm{a})$ the acceleration of the object, (b) the angular momentum of the object about the origin, (c) the torque about the origin acting on the object, and (d) the angle between the velocity of the object and the force acting on the object.

Question

A time-dependent torque given by $\tau=a+b$ sin $c t$ is applied to an object that's initially stationary but is free to rotate. Here $a, b$ and $c$ are constants. Find an expression for the object's angular momentum as a function of time, assuming the torque is first applied at $t=0$.

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