AP Physics 1: Chapter 8: Rotational Equilibrium and Dynamics

For the wheel-and-axle system shown above, which of the following expresses the condition required for the system to be in static equilibrium?

A bowling ball of mass M and radius R. whose moment of inertia about its center is $$\frac{2}{5}MR^2$$ , rolls without slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an incline is

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above.

If the plane is frictionless, what is the speed $$v_{cm}$$ , of the center of mass of the sphere at the bottom of the incline?

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above.

If the plane has friction so that the sphere rolls without slipping, what is the speed $$v_{cm}$$ of the center of mass at the bottom of the incline?

A uniform rigid bar of weight W is supported in a horizontal orientation as shown above by a rope that makes a 30° angle with the horizontal. The force exerted on the bar at point O, where it is pivoted, is best represented by a vector whose direction is which of the following?

A rod of negligible mass is pivoted at a point that is off-center, so that length $$l_1$$ is different from length $$l_2$$ . The figures above show two cases in which masses are suspended from the ends of the rod. In each case the unknown mass m is balanced by a known mass, $$M_1$$ or $$M_2$$ , so that the rod remains horizontal. What is the value of m in terms of the known masses?

A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown above. The magnitude of the net torque on the system about the axis is:

Two blocks are joined by a light string that passes over the pulley shown above, which has radius R and moment of inertia I about its center. $$T_1$$ and $$T_2$$ are the tensions in the string on either side of the pulley and α is the angular acceleration of the pulley. Which of the following equations best describes the pulley's rotational motion during the time the blocks accelerate?

A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval $$\Delta t$$ and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is $$\frac{1}{2}MR^2$$ .

The net force on the cylinder during the time interval $$\Delta t$$ is:

A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval $$\Delta t$$ and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is $$\frac{1}{2}MR^2$$ .

The linear acceleration of the person's hand during the time interval $$\Delta t$$ is: