Newton’s First & Second Law in Rotational Form (College Board AP® Physics 1: Algebra-Based): Exam Questions

Two masses, $m_1=5\mathrm{kg}$ and $m_2=3\mathrm{kg}$, are suspended by a light, inextensible rope that goes over a pulley of radius $R=0.2\mathrm{m}$ and mass $M=10\mathrm{kg}$, as shown in the figure. The rotational inertia of the pulley is $I=\frac{1}{2}M{R}^2$. The pulley can rotate about its center with negligible friction. Initially, mass $m_2$ is on the ground, and mass $m_1$ is suspended at a height $h$above the ground.

When the masses are released, which of the following is most nearly the angular acceleration of the pulley?

A system of two wheels, of radii $2R$ and $3R$ respectively, are joined together and free to rotate about a frictionless axis through their common center. Four forces are exerted tangentially to the rims of the wheels, as shown in the figure.

Which of the following correctly represents the magnitude of the net torque on the system about the axis?

A disk is initially rotating counterclockwise around a fixed axis with angular speed ${\omega }_0$. At time $t$ = 0, two forces are exerted on the disk as shown in the figure.

Taking counterclockwise as the positive direction, which of the following is the best representation of the angular velocity of the disk as a function of time?

A uniform rod of mass $M$ and length $L$ is free to rotate about a pivot at its left end and is released from rest when the rod is 60° above the horizontal, as shown in the figure. The angular acceleration of the rod is ${\alpha }_0$at the moment it is released.

Which of the following expressions correctly represents the magnitude of the angular acceleration of the rod at the moment it passes through the horizontal position?

An object of mass $m$ is placed at the 20 cm mark on a uniform meterstick of mass $1.5m$.

If an object of mass $2m$is placed at the 90 cm mark, which of the following points on the meterstick should the fulcrum be placed to balance the system?

Blocks A and B, of masses $m_A$ and $m_B$, respectively, are joined by a light string that passes over a pulley, as shown in the figure. The pulley has a radius $R$ and a rotational inertia $\frac{1}{2}M{R}^2$ about its center. The string does not slip on the pulley as Block B accelerates along the horizontal frictionless surface and Block A accelerates vertically downwards.

Which of the following gives the magnitude of the linear acceleration of the blocks?

A hollow sphere of mass $1\mathrm{kg}$ and radius $R=0.5\mathrm{m}$ is attached to the end of a thin uniform rod of mass $3\mathrm{kg}$ and length $L=1.5\mathrm{m}$. The rod is free to rotate about a pivot at its left end and held horizontally by a string at its right end, as shown in the figure. With respect to the pivot, the rod has rotational inertia $\frac{1}{3}M{L}^2$. The rotational inertia of a hollow sphere about its center is $\frac{2}{3}M{R}^2$.

If the string breaks, which of the following is most nearly the angular acceleration of the rod immediately after the system is released?

Objects A and B, of masses $M_A$ and $M_B$ respectively, are attached to a light rigid rod, as shown in the figure. When the system is released from rest, it begins to rotate counterclockwise about the pivot with angular acceleration $\frac{g}{7L}$.

Which of the following expressions correctly represents the mass of object A?

A thin uniform ladder of length $L$ rests against a frictionless wall at an angle $\theta$, as shown in the figure. The coefficient of friction between the ladder and the ground is $\mu$.

Which of the following expressions gives the minimum value of $\mu$ required to stop the ladder from sliding?

Two masses, $m_1$ and $m_2$, are attached to light strings which are wound around two frictionless pulleys of radii $r$ and $2r$ respectively, which are free to rotate about the same axle at their centers, as shown in the figure. When mass $m_1$ is placed on a frictionless ramp that makes an angle $\theta$ with the horizontal and mass $m_2$ is suspended from the pulley, the system is in static equilibrium.

Which of the following expressions correctly relates the sizes of the two masses?