Rotational Physics

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?

• It would decrease because the force of friction would be greater.

• It would decrease because the net torque would be larger.

• It would increase because the angular acceleration would increase.

• It would increase because the linear acceleration would increase.

• It would remain the same because the net torque would remain the same.

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

• b

• c

• d

• The spool will roll on the table for all four directions shown

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?

• From t = 0 s to t = 1 s

• From t = 1 s to t = 3 s

• From t = 3 s to t = 5 s

• From t = 5 s to t = 7 s

• From t = 7 s to t = 8 s

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?

• mbt/r

• mbrt

• mbr²t

• mbr²rt²

• mb²r²t²

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

• 2MR²

• 3MR²

• 4MR²

• 5MR²

• 10MR²

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

• (T - mg)/m

• 2g

• g/2

• T/m

• zero

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?

• 0.00 s

• 1.00 s

• 1.75 s

• 2.50 s

When a fan performing 10 revolutions per second is switched off, it comes to rest after 10 seconds. Calculate the magnitude of the average angular acceleration of the fan after it was switched off.

• 1 rad/s2

• 2π rad/s2

• π rad/s2

• 10 rad/s2

What does the area of a  $\alpha$  vs t graph represent?

• The angular acceleration ( $\alpha$  )

• The change in angular velocity ( $\Delta\omega$  )

• The angular displacement ( $\Delta\theta$  )

• The torque ( $\tau$  )

A flywheel starts from rest, and has an angular acceleration of 4 rad/s². What will be its angular speed when it has made 2 revolutions?

• 7.09 rad/s

• 6.35 rad/s

• 10.03 rad/s

• 5.01 rad/s