Relationship Between Torque and Angular Acceleration

20. The quantity “moment of inertia” (in terms of the fundamental quantities of mass, length, and time) is equivalent to:

a. ML2T2. b. ML. c. ML2_.

d. ML1T2.

21. A 4.2-kg mass is placed at (3.0, 4.0) m. Where can an 8.4-kg mass be placed so that the moment of inertia about the =-axis is zero?

a. (-3.0, -4.0) m b. (-6.0, -8.0) m c. (-1.5, -2.0) m

d. There is no position giving this result.

22. A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the <-axis?

a. 160 kg·m2

b. 90 kg·m2

c. 250 kg·m2

d. 32 kg·m2

23 A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the 7-axis?

a. 160 kg·m2

b. 90 kg·m2

c. 250 kg·m2

d. 180 kg·m2

24. A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the =-axis?

a. 160 kg·m2

b. 90 kg·m2

c. 250kg·m2

d. 180 kg·m2

25. If a net torque is applied to an object, that object will experience: a. a constant angular speed.

b. an angular acceleration. c. a constant moment of inertia. d. an increasing moment of inertia.

26. According to Newton’s second law, the angular acceleration experienced by an object is directly proportional to:

a. its moment of inertia. b. the net applied torque. c. the object’s size.

d. choices a and b above are both valid.

27. A ventilation fan with a moment of inertia of 0.034 kg˜m2 _{has a net torque of 0.11 N˜m}

applied to it. What angular acceleration does it experience? a. 5.3 rad/s2

b. 4.0 rad/s2

c. 3.2 rad/s2

d. 0.31 rad/s2

28. A disk has a moment of inertia of 3.0 u 104 _kg˜m2 _{and rotates with an angular speed of 3.5}

rad/sec. What net torque must be applied to bring it to rest within 3 s? a. 4.5 u 103 _N˜m

b. 7.5 u 104 _N˜m

c. 3.5 u 104 _N˜m

d. 5.0 u 104 _N˜m

29. The Earth moves about the Sun in an elliptical orbit. As the Earth moves closer to the Sun, which of the following best describes the Earth-Sun system’s moment of inertia?

a. decreases b. increases c. remains constant

d. none of the above choices are valid

30. A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 u 102 _kg˜m2 _{and a radius of}

0.10 m. If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its angular speed?

a. 0.80 rad/s b. 10 rad/s c. 0.050 rad/s d. 40 rad/s

31. A baseball pitcher, loosening up his arm before a game, tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s, what is the average angular acceleration of the arm and ball?

a. 0.067 rad/s2

b. 94 rad/s2

c. 15 rad/s2

d. 37 rad/s2

32. A baseball pitcher loosens up his pitching arm. He tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball. What is the moment of inertia of the ball alone as it moves in a circular arc with a radius of 0.32 m?

a. 1.5 u 102 _kg˜m2

b. 16 u 102 _kg˜m2

c. 4.0 u 102 _kg˜m2

d. 7.6 u 102 _kg˜m2

33. A baseball pitcher loosens up his pitching arm. He tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s, what torque is applied to the ball while being held by the pitcher’s hand to produce the angular acceleration?

a. 1.1 N˜m b. 11 N˜m c. 7.2 N˜m d. 1.4 N˜m

34. A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.12 kg˜m2_{. If the bucket is raised to the top of the well and released, what is the acceleration of}

the bucket as it falls toward the bottom of the well? (Assume rope’s mass is negligible, that cylinder turns on frictionless bearings and that ; = 9.8 m/s2_.)

a. 3.2 m/s2

b. 6.3 m/s2

c. 7.4 m/s2

d. 9.8 m/s2

35. A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well. The bucket is raised to the top of the well and released. The bucket is moving with a speed of 8.0 m/s upon hitting the water surface in the well. What is the angular speed of the cylinder at this instant?

a. 39 rad/s b. 79 rad/s c. 120 rad/s d. 160 rad/s

36. A majorette takes two batons and fastens them together in the middle at right angles to make an “x” shape. Each baton was 0.80 m long and each ball on the end is 0.20 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?

a. 0.048 kg˜m2

b. 0.064 kg˜m2

c. 0.19 kg˜m2

d. 0.32 kg˜m2

37. A majorette takes two batons and fastens them together in the middle at right angles to make an “x” shape. Each baton was 0.80 m long and each ball on the end is 0.20 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?

a. 0.064 kg˜m2

b. 0.096 kg˜m2

c. 0.13 kg˜m2

d. 0.32 kg˜m2

38. A solid cylinder (> = ?+2_{/2) has a string wrapped around it many times. When I release the}

cylinder, holding on to the string, the cylinder falls and spins as the string unwinds. What is the downward acceleration of the cylinder as it falls?

a. 0 b. 4.9 m/s2

c. 6.5 m/s2

d. 9.8 m/s2

39. A 40-kg boy is standing on the edge of a stationary 30-kg platform that is free to rotate. The boy tries to walk around the platform in a counterclockwise direction. As he does:

a. the platform doesn’t rotate.

b. the platform rotates in a clockwise direction just fast enough so that the boy remains stationary relative to the ground.

c. the platform rotates in a clockwise direction while the boy goes around in a counterclockwise direction relative to the ground.

d. both go around with equal angular velocities but in opposite directions.

40. A rod of length @ is hinged at one end. The moment of inertia as the rod rotates around that hinge is ?@2_{/3. Suppose a 2.00-m rod with a mass of 3.00 kg is hinged at one end and is held}

in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released?

a. 3.70 rad/s2

b. 7.35 rad/s2

c. 2.45 rad/s2

d. 4.90 rad/s2

41. Two hoops or rings (> = ?+2) are centered, lying on a turntable. The smaller ring has radius = 0.050 m; the larger has radius = 0.10 m. Both have a mass of 3.0 kg. What is the total

moment of inertia as the turntable spins? Ignore the mass of the turntable. a. 0.030 kg˜m2

b. 0.007 5 kg˜m2

c. 0.038 kg˜m2

d. 0.075 kg˜m2

42. An automobile accelerates from zero to 30 m/s in 6.0 s. The wheels have a diameter of 0.40 m. What is the average angular acceleration of each wheel?

a. 5.0 rad/s2

b. 15 rad/s2

c. 25 rad/s2

d. 35 rad/s2

43. An object consists of a rod (of length 3.0 m and negligible moment of inertia) to which four small 2.0-kg masses are attached, one at each end and one at each point on the rod 1.0 m from each end. (The masses are one meter apart.) The moment of inertia of this object about an axis perpendicular to the rod and through one of the inner masses:

a. is 72 kg˜m2_.

b. is 12 kg˜m2_.

c. is 4 kg˜m2_.

d. cannot be uniquely determined until it is stated which inner mass the axis goes through.