Practice Questions: Torque, Rotation and Angular Momentum 36. A satellite that is a spinning cylinder has initial rotational inertia Io and angular velocity ωo.

Solar panels unfold from the satellite and are extended outward. The satellite then has

rotational inertia If = aIo and angular velocity wf = bωo, where a and b are constants. Which of

the following is true about the constants a and b ? (A) a = 1 and b = 1 (B) a > 1 and b < 1 (C) a > 1 and b = 1 (D) a < 1 and b < 1

46. A uniform plank is placed with a pivot at its center. A block is placed on the plank to the left of the pivot, as shown in the figure above. A student is asked to place a second block of greater mass on the plank so it will balance when horizontal. Which of the following quantities are needed to determine where the second block should be placed? Select two answers. (A) The mass of the plank (B) The mass of each block (C) The length of the plank (D) The distance from the pivot to the left block

33. The toy car shown in the figure above enters the vertical circular loop with an initial velocity and

moves completely around the loop without friction. If the car has no means of self-propulsion, which of

the following is true of the car’s acceleration at the instant it is at point P ?

(A) It is vertically upward.

(B) It is in the direction of the velocity.

(C) It is directly toward the center of the circle.

(D) It has components both downward and toward the center of the circle.

(E) It has components both downward and away from the center of the circle.

40. A nonrotating spherical planet with no atmosphere has mass M and radius R. A projectile of mass m

is launched radially from the surface of the planet with initial speed . The potential energy

of the projectile-planet system, as a function of the projectile’s distance r from the center of the

planet, is given by The greatest distance from the center of the planet that the projectile

reaches is

(A) infinity (B) R (C) 7/5 R (D) 4/3 R (E) R

41. The radius of an asteroid’s orbit about the Sun is approximately 2 times the radius of Earth’s orbit

about the Sun. The time, measured in Earth years, for the asteroid to make one complete revolution about

the Sun is most nearly

(A) 1.4 years (B) 2.0 years (C) 2.8 years (D) 4.0 years (E) 8.0 years

1. A car with a mass of 1500 kg is driving at a constant speed around a corner with a constant radius.

a. Draw a free body diagram of the car. Label all of the forces acting on the car.

b. If the radius of the corner is 20 m and the speed of the car is 10 m/s, what is the car’s lateral acceleration? Is this a realistic value for a normal car on a normal road? Explain.

c. If the coefficient of friction between the tires and the road is 0.8, what is the maximum speed for any car around this road?

2. At a science museum there is an activity where guests can pick up a 2500 kg truck attached to a 20 m long beam like the diagram below.

a. Mark an ‘x’ on the horizontal beam where the fulcrum should be. Justify your answer.

b. If a guest has a mass of 50 kg, and they and the truck are attached to the beam at opposite ends, where exactly should the fulcrum be (ignore the mass of the beam)?

Answers 36: B 46: B, D 33: 40: 41: