5. Rotation Dynamics

Torque And Equations — Quiz

Test your understanding of torque and equations with 5 practice questions.

Practice Questions

Question 1

A uniform rod of mass $M$ and length $L$ is pivoted at one end. If the rod is released from rest in a horizontal position, what is its initial angular acceleration?

Question 2

An object's angular velocity is given by the function $\omega(t) = 3t^2 - 4t + 2$, where $\omega$ is in rad/s and $t$ is in seconds. What is the angular displacement of the object from $t = 1 \text{ s}$ to $t = 3 \text{ s}$?

Question 3

A uniform solid sphere of mass $M$ and radius $R$ is subjected to a constant net torque $\tau$. If it starts from rest, what is its angular velocity after time $t$?

Question 4

A force $\vec{F} = (2\hat{i} - 3\hat{j}) \text{ N}$ is applied at a position vector $\vec{r} = (4\hat{i} + \hat{j}) \text{ m}$ from the pivot point. What is the magnitude of the torque produced?

Question 5

If the angular acceleration of an object is given by $\alpha(t) = 12t^2 - 6t$, and its initial angular position at $t = 0 \text{ s}$ is $\theta_0 = 0 \text{ rad}$ and initial angular velocity is $\omega_0 = 3 \text{ rad/s}$, what is the angular position $\theta(t)$ as a function of time?