Four round objects of equal mass and radius roll without slipping along a horizontal surface that then bends upward and backward into an arc of half a circle. The objects all have the same linear speed initially. The objects are a hollow cylinder, a solid cylinder, a solid sphere, and a hollow sphere. The objects to go up the arc and exit the arc going in the opposite direction they entered without falling off the arc. Now, several trials are run for each object. For each trial, the initial speed of the object is reduced until the object does not make it through the full arc. The speed needed for each object to just make it through the arc is recorded. Which of the following correctly lists the objects in order from fastest to slowest speed needed to make it through the arc?

A small solid sphere is released from rest at the top of an inclined plane as shown. The sphere rolls down without slipping and reaches the bottom of the plane. How would the angular momentum of the sphere at the bottom of the plane change if the coefficient of static friction between the sphere and the plane were increased?

A spool is made of two circular disks connected to the ends of a cylinder so that the centers of the disks and the cylinder are aligned. In the figure above, the cylinder is shown as the dashed circle, and the disk on one end of the cylinder is shown as the larger solid circle. The spool is at rest on a level horizontal surface. A string attached to the cylinder is pulled gently so that the spool can rotate without slipping on the surface at point P. A force F

is pulled in the direction of arrow d

, and the spool spins but does not roll across the table. If the string is pulled with a force of 2F

, which of the directions indicated, if any, indicates a pull on the string that will cause the spool to spin but not roll across the table?

A motor drives a shaft of radius R/8 that is attached to the center of a wheel of radius R. The motor is turned off, and the force that the motor exerts on the shaft, F_motor, varies with time, as shown. There is also a constant friction force of 0.4N applied to the rim of the wheel in the opposite direction of the motion. During which time interval does the rotational kinetic energy increase and then decrease?

Given the graph above of angular acceleration versus time for a rigid body rotating about a fixed axis, which segment of the graph represents the time interval during which the largest magnitude of net torque is exerted on the rigid body?

An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity 𝜔 . As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight.

What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III?

A particle of mass m moves counterclockwise around a horizontal circle of radius r, as shown above. The angular speed of the particle is given as a function of time t by ω (t) = bt , where b is a positive constant and t ≥ 0.

What is the magnitude of the angular momentum of the particle about the center of the circle as a function of time?

A solid disk of mass M and radius R is freely rotating horizontally in a counterclockwise direction with angular speed ω about a vertical axis through its center with negligible friction. The rotational inertia of the disk is MR²/2. A second identical disk is at rest and suspended above the first disk with the centers of the two disks aligned, as shown in the figure above. There is no contact between the disks. The second disk is dropped onto the first disk, and after a short time they rotate counterclockwise with the same angular speed ωf.

The two disks are now shifted so that the axis of rotation goes through a point on the edge of the disks. The rotational inertia of the two-disk system is now

The rotational inertia of a sphere of mass M and radius R about a diameter is 2/5 MR². The rotational inertia about an axis tangent to the sphere is

A uniform ladder of weight W leans without slipping against a wall making an angle 𝜽 with a floor as shown above. There is friction between the ladder and the floor, but the friction between the ladder and the wall is negligible.

The magnitude of the friction force exerted on the ladder by the floor 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 Δt 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 1/2 mR². The linear acceleration of the person's hand during the time interval Δt is

A wheel of radius R is fixed to an axle of radius R/3 and rotates at constant angular speed ω , as shown in the figure above. A force of magnitude F₁ is applied tangent to the outer edge of the wheel. A second force of magnitude F₂ is applied tangent to the edge of the axle to keep the wheel rotating at constant angular speed ω. The magnitude F₂ is equal to

A disk-shaped platform has a known rotational inertia I_D. The platform is mounted on a fixed axle and rotates in a horizontal plane with an initial angular velocity of ω_D in the counterclockwise direction, as shown. After an unknown time interval, the disk comes to rest. A single point on the disk revolves around the center axle hundreds of times before the disk comes to rest. Frictional forces are considered to be constant.

A student must determine the angular impulse that frictional forces exert on the disk from the moment it rotates with angular velocity in the counterclockwise direction until it stops. What additional data, if any, should a student collect to determine the angular impulse on the disk? Justify your selection.

A disk-shaped platform has a known rotational inertia I_D. The platform is mounted on a fixed axle and rotates in a horizontal plane with an initial angular velocity of ω_D in the counterclockwise direction, as shown. After an unknown time interval, the disk comes to rest. A single point on the disk revolves around the center axle hundreds of times before the disk comes to rest. Frictional forces are considered to be constant.

A student must determine the angular impulse that frictional forces exert on the disk from the moment it rotates with angular velocity ω_D in the counterclockwise direction until it stops. Which of the following could the student have used in order to approximate the initial angular velocity of the rotating disk?

A ball of mass M swings in a horizontal circle at the end of a string of radius R at an initial tangential speed v₀ as it undergoes uniform centripetal motion. A student gradually pulls the string inward such that the radius of the circle decreases, as shown in the figure.

Which of the following predictions is correct regarding the angular momentum and rotational inertia of the ball about the axis of revolution as the ball is pulled inward?

A horizontal disk of radius 0.2m and mass 0.3kg is mounted on a central vertical axle so that a student can study the relationship between net torque and change in angular momentum of the disk. In the experiment, the student uses a force probe to collect data pertaining to the net torque exerted on the edge of the disk as a function of time, as shown in the graph. The disk is initially at rest. At what instant in time does the disk have the greatest angular momentum?

The rotational inertia of an object is greater when most of the mass is located

For round objects rolling on an incline, the faster objects are generally those with the

For an object traveling in a circular path, its angular momentum doubles when its linear speed