A uniform meterstick is balanced at the center, as shown above. Which of the following shows how a 0.50 kg mass and a 1.0 kg mass could be hung on the meterstick so that the stick stays balanced?

A uniform ladder of mass M and length L rests against a smooth wall at an angle  $\theta_0$  , as shown in the figure. What is the torque due to the weight of the ladder about its base?

An object rotates with an angular speed that varies with time, as shown in the graph. How can the graph be used to determine the magnitude of the angular acceleration α of the object? Justify your selection.

Two small objects of mass m₀ and a rotating platform of radius R and rotational inertia I_p about its center compose a single system. Students use the system to conduct two experiments. The objects are assumed to be point masses.

Each object of mass m₀ is placed a distance r₁ away from the center of the platform such that both masses are on opposite sides of the platform. A constant tangential force F₀ is applied to the edge of the platform for a time Δt₀, as shown in Figure 1. The system is initially at rest.

Each object of mass m₀ is placed a distance r₂ away from the center of the platform such that both masses are on opposite sides of the platform. Distance r₂<r₁ . A constant tangential force F₀ is applied to the edge of the platform for a time Δt₀, as shown in Figure 2. The system is initially at rest.

Which of the following graphs represents the angular displacement of the system as a function of time for the system in experiment 1?

A graph of the angular velocity ω as a function of time t is shown for an object that rotates about an axis. Three time intervals, 1–3, are shown. Which of the following correctly compares the angular displacement Δθ of the object during each time interval?

A uniform horizontal beam of mass M and length  $L_0$   is attached to a hinge at point P, with the opposite end supported by a cable, as shown in the figure. The angle between the beam and the cable is  $\theta_0$  . What is the magnitude of the torque that the cable exerts on the beam?

One end of a string is attached to the ceiling, and the other end of the string is attached to a cradle that has a meterstick that runs through it. The meterstick can slide through the cradle so that the horizontal position of a point on the meterstick can be changed in the horizontal direction. Students may hang objects of various masses from the meterstick. The students notice that when the meterstick-cradle-object-object system is not balanced, the meterstick will rotate.

Consider the situation shown in the image in which the center of the meterstick is aligned with the center of the cradle, which is at a position of x = 0m. The system is released from rest. Which of the following claims is correct about the motion of the system containing the meterstick, cradle, and two objects if the system is free to rotate?

A disk of radius 50 cm rotates about a center axle. The angular position as a function of time for a point on the edge of the disk is shown. Which two of the following quantities of the point on the edge of the disk can be correctly mathematically determined from the graph using the methods described? Justify your selections. Select TWO answers.

The graph shows the angular velocity ω as a function of time t for a point on a rotating disk. The magnitude of the angular acceleration of the disk at t=2s is most nearly

A horizontal, uniform board of weight 125 N and length 4 m is supported by vertical chains at each end. A person weighing 500 N is sitting on the board. The tension in the right chain is 250 N.

How far from the left end of the board is the person sitting?

A uniform, rigid rod of length 2 m lies on a horizontal surface. One end of the rod can pivot about an axis that is perpendicular to the rod and along the plane of the page. A 10 N force is applied to the rod at its midpoint at an angle of 37°. A second force F is applied to the free end of the rod so that the rod remains at rest, as shown in the figure. The magnitude of the torque produced by force F is most nearly

A disk is initially rotating counterclockwise around a fixed axis with angular speed ω₀.

At time t = 0, the two forces shown in the figure above are exerted on the disk. If counterclockwise is positive, which of the following could show the angular velocity of the disk as a function of time?

The figures below indicate forces acting on a rod in different situations. The lengths of the force vectors are proportional to the magnitudes of the forces. In which situation is the rod in both translational and rotational equilibrium?

Two identical wheels, wheel 1 and wheel 2, initially at rest begin to rotate with constant angular accelerations  $\alpha$ . After rotating through the same angular displacement,  $\Delta\theta_0$ , the angular velocity of wheel 1 is  $\omega_1$  and the angular velocity of wheel 2 is  $\omega_2=3\omega_1$ . How does the angular acceleration of wheel 2,  $\alpha_2$  , compare to the angular acceleration of wheel 1,  $\propto_1$  ?