AP Physics C Mechanics Quiz: Newtons Second Law In Rotational Form

A rigid body with rotational inertia $I$ experiences a net torque $\tau$, resulting in an angular acceleration $\alpha$. If the mass of the body is doubled, with its shape and dimensions remaining identical, what is the new angular acceleration for the same net torque $\tau$?

A solid disk and a hoop have the same mass $M$ and radius $R$. They are both initially at rest and are free to rotate about a fixed, frictionless axle through their centers. The same constant net torque is applied to both. After one second, which of the following correctly compares their angular accelerations, $\alpha_{disk}$ and $\alpha_{hoop}$?

A solid sphere is rolling without slipping on a horizontal surface. A horizontal force $F$ is applied to the center of the sphere, causing it to accelerate. Static friction $f$ acts on the sphere. The sphere has mass $M$, radius $R$, and rotational inertia $I=\frac{2}{5}MR^2$. Which equation correctly applies Newton's second law for rotation about the sphere's center of mass?

A thin, uniform rod of mass $M$ and length $L$ is pivoted at one end and hangs vertically. It is displaced by a small angle $\theta$ from the vertical and released. What is the magnitude of its initial angular acceleration? The rotational inertia of the rod about its end is $I = \frac{1}{3}ML^2$.

A uniform solid cylinder of mass $M$ and radius $R$ rolls without slipping down an incline that makes an angle $\theta$ with the horizontal. The rotational inertia of the cylinder is $I = \frac{1}{2}MR^2$. What is the angular acceleration of the cylinder?

A large turntable with rotational inertia $I$ is rotating at a constant angular velocity. A person walks from the center of the turntable towards the rim. The frictional force between the person's shoes and the turntable provides the necessary torque for the person to accelerate angularly. By Newton's third law, the person exerts an equal and opposite torque on the turntable. This reaction torque causes the turntable's angular velocity to:

A solid disk is suspended by a thin wire attached to its center, forming a torsional pendulum. When twisted from its equilibrium position by an angle $\theta$, the wire exerts a restoring torque $\tau = -\kappa\theta$, where $\kappa$ is the torsion constant. The rotational inertia of the disk is $I$. What is the differential equation that describes the angular motion of the disk?

A uniform horizontal disk of mass $M$ and radius $R$ is rotating freely about a vertical axis through its center with angular speed $\omega$. A small piece of putty of mass $m$ is dropped vertically and sticks to the disk at a distance $r$ from the center. During the collision, the putty exerts a torque on the disk. The torque is due to:

Torque is $\tau = rF\sin\theta$ and $\tau_{\text{net}} = I\alpha$ connects net torque to angular acceleration. A disc has $I=0.50\,\text{kg\u00b7m}^2$ and two tangential forces act at the rim: $8\,\text{N}$ clockwise and $3\,\text{N}$ counterclockwise at $r=0.25\,\text{m}$. What is $\alpha$ (clockwise positive)?

Torque is $\tau = rF\sin\theta$ and rotational Newton's Second Law is $\tau_{\text{net}} = I\alpha$. A disc experiences $\tau_{\text{net}}=9.0\,\text{N\u00b7m}$ and $\alpha=3.0\,\text{rad/s}^2$. Determine the moment of inertia $I$.

Torque is $\tau = rF\sin\theta$ and rotational Newton's Second Law is $\tau_{\text{net}} = I\alpha$, where $I$ resists changes in rotation. A wheel has $I=2.0\,\text{kg\u00b7m}^2$ and experiences a net torque $\tau_{\text{net}}=6.0\,\text{N\u00b7m}$. Calculate the angular acceleration $\alpha$.

Torque is defined as $\tau = rF\sin\theta$ and rotational dynamics follow $\tau_{\text{net}} = I\alpha$. A rotating disc has $I=0.80\,\text{kg\u00b7m}^2$ and angular acceleration $\alpha=2.5\,\text{rad/s}^2$. If net torque causes this change, what is $\tau_{\text{net}}$?

Torque is $\tau = rF\sin\theta$ and rotational Newton's Second Law is $\tau_{\text{net}} = I\alpha$. A tangential force $F=15\,\text{N}$ is applied at $r=0.20\,\text{m}$ to a disc with $I=0.30\,\text{kg\u00b7m}^2$. Calculate the angular acceleration $\alpha$.

A wheel's torque is $\tau=rF\sin\theta$ and also $\tau=I\alpha$. If $\alpha=4.0\,\text{rad/s}^2$ and $I=0.75\,\text{kg·m}^2$, what is $\tau_{\text{net}}$?

A disc's torque is $\tau=rF\sin\theta$ and $\tau=I\alpha$. With $r=0.40\,\text{m}$, $F=20\,\text{N}$ tangential, and $I=2.0\,\text{kg·m}^2$, calculate $\alpha$.

A uniform solid disk of mass $M$ and radius $R$ is free to rotate about a frictionless axle through its center. A constant tangential force $F$ is applied to the edge of the disk. The rotational inertia of a solid disk about its center is $I = \frac{1}{2}MR^2$. What is the magnitude of the angular acceleration of the disk?

A thin, uniform rod of mass $M$ and length $L$ is pivoted at one end. It is held horizontally and released from rest. The rotational inertia of the rod about its end is $I = \frac{1}{3}ML^2$. What is the initial angular acceleration of the rod immediately after release?

An Atwood machine consists of two blocks of mass $m_1$ and $m_2$ ($m_1 > m_2$) connected by a light string over a solid disk pulley of mass $M$ and radius $R$. The string does not slip, and the pulley has rotational inertia $I = \frac{1}{2}MR^2$. What is the magnitude of the pulley's angular acceleration?

A flywheel with rotational inertia $I$ is rotating with angular velocity $\omega_0$. A constant frictional torque $\tau_f$ is exerted on the axle, causing the flywheel to slow down and stop. The angular acceleration $\alpha$ of the flywheel is:

A time-varying torque given by $\tau(t) = kt^2$, where $k$ is a positive constant, is applied to a rigid body with rotational inertia $I$. The body starts from rest at $t=0$. What is the angular acceleration of the body as a function of time?