## Related questions with answers

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

Solution

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

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

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

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

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

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

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

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

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

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

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

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