(Multiple choice)

(1) True or false:

If the net torque on a rotating system is zero, the angular velocity of the system cannot change.

(2)

If the angular momentum of a system is constant, which of the following statements must be true? 

(a) No torque acts on any part of the system. 

(b) A constant torque acts on each part of the system. 

(c) Zero net torque acts on each part of the system. 

(d) A constant external torque acts on the system. 

(e) Zero net torque acts on the system.

(3)

Two identical cylindrical disks have a common axis. Initially, one of the disks is spinning. When the two disks are brought into contact they stick together. Which of the following statements is true? 

(a) The total kinetic energy and the total angular momentum are unchanged from their initial values. 

(b) Both the total kinetic energy and the total angular momentum are reduced to half of their original values. 

(c) The total angular momentum is unchanged, but the total kinetic energy is reduced to half its original value. 

(d) The total angular momentum is reduced to half of its original value, but the total kinetic energy is unchanged. 

(e) The total angular momentum is unchanged, and the total kinetic energy is reduced to one-quarter of its original value.

(4)

A block sliding on a frictionless table is attached to a string that passes through a hole in the table. Initially, the block is sliding with speed v₀ in a circle of radius r₀. A student under the table pulls slowly on the string. What happens as the block spirals inward? Give supporting arguments for your choice. 

(a) Its energy and angular momentum are conserved. 

(b) Its angular momentum is conserved, and its energy increases. 

(c) Its angular momentum is conserved, and its energy decreases. 

(d) Its energy is conserved, and its angular momentum increases. 

(e) Its energy is conserved, and its angular momentum decreases.

(5)

Under gravitational collapse (all forces on various pieces are inward toward the center), the radius of a spinning spherical star of uniform density shrinks by a factor of 2, with the resulting increased density remaining uniform throughout as the star shrinks. What will be the ratio of the final angular speed ω₂ to the initial angular speed ω₁?

(a) 2

(b) 0.5 

(c) 4

(d) 0.25 

(e) 1.0

(6) True / False

(a) Nutation and precession are the same phenomenon. 

(b) The direction of precession is the direction of the net torque. 

(c) When the gyroscope is not spinning, τ = dL/dt does not hold.