Question

O A constant nonzero net torque is exerted on an object. Which of the following can not be constant? Choose all that apply. (a) angular position (b) angular velocity (c) angular acceleration (d) moment of inertia (e) kinetic energy (f) location of the center of mass

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The relationship between the net torque M\vec{M} that acts on a body with the moment of inertia II and the angular acceleration α\vec{\alpha} is given by:

Iα=M\begin{align*} I\vec{\alpha}=\vec{M} \end{align*}

Hence, if the torque M\vec{M} is constant, so must be the angular acceleration α\alpha and the moment of inertia II.

Since the angular velocity ω\vec{\omega} is related to the (now constant) angular acceleration α\vec{\alpha} by

α=dωdt=const\begin{align*} \vec{\alpha}=\frac{d\vec{\omega}}{dt}=\vec{const} \end{align*}

we conclude that ω\vec{\omega} is not constant.

Since the angular position r\vec{r} is related to the (now constant) angular acceleration α\vec{\alpha} by

α=dωdt=d2rdt2=const\begin{align*} \vec{\alpha}=\frac{d\vec{\omega}}{dt}=\frac{d^2r}{dt^2}=\vec{const} \end{align*}

we conclude that r\vec{r} is not constant.

As for the kinetic energy KK, it is also not constant since the angular velocity ω\vec{\omega} is not constant.

As for the location of the centre of mass rCM\vec{r_{CM}}, since the object does not need to be homogenous, rCM\vec{r_{CM}} does not need to be constant.

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