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Gwendoline Gaines
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1 Quiz Torque Name 1) A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of m from his shoulder. What is the torque on the shoulder joint if the arm is horizontal? A) 4.40 Nm B) 43.2 Nm C) 14.5 Nm D) 0 Nm 2) A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop. If the wheel has a moment of inertia of kg m 2, and the wheel slows to a stop in 160 s, what is the magnitude of the retarding torque? A) 1.00 Nm B) Nm C) 1.33 Nm D) 1.67 Nm 3) A mass of 375 g hangs from a string that is wrapped around the circumference of a pulley with a moment of inertia of kg m 2 and a radius of 26.0 cm. When the mass is released, the mass accelerates downward and the pulley rotates about its axis as the string unwinds. What is the acceleration of the mass? A) 19.9 m/s 2 B) 13.1 m/s 2 C) 6.57 m/s 2 D) 3.28 m/s 2 4) The L-shaped object shown in Figure 11-6 consists of the masses connected by light rods. How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s about the x-axis? A) 23.7 J B) 17.6 J C) 47.4 J D) 34.2 J Answer: D 5) When you ride a bicycle, in what direction is the angular velocity of the wheels? A) to your left B) to your right C) forwards D) backwards 1

2 2 6) The drive chain in a bicycle is applying a torque of Nm to the wheel of the bicycle. Treat the wheel as a hoop with a mass of kg and a radius of 33.0 cm. What is the angular acceleration of the wheel? A) 10.4 rad/s 2 B) 5.20 rad/s 2 C) 3.43 rad/s 2 D) 1.06 rad/s 2 7) A person sits on a freely spinning lab stool (no friction). When this person extends her arms, A) her moment of inertia decreases and her angular velocity increases. B) her moment of inertia decreases and her angular velocity decreases. C) her moment of inertia increases and her angular velocity increases. D) her moment of inertia increases and her angular velocity decreases. Answer: D 8) An ice skater doing a spin pulls in her arms, decreasing her moment of inertia by a factor of two. How does her angular speed changes? A) It is reduced by a factor of two. B) It is reduced by a factor of four. C) It increases by a factor of two. D) It increases by a factor of four. Answer: C 9) What is the correct expression for torque, in terms of the magnitude of the force, F, the radial distance from the axis of rotation, r, and the angle between the force and the radial line, θ? A) τ = F r sinθ B) τ = F r cosθ C) τ = F r tanθ D) τ = F r θ 10) A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of m from his shoulder. What is the torque on the shoulder joint if the arm is horizontal? A) 4.40 Nm B) 43.2 Nm C) 14.5 Nm D) 0 Nm 11) Consider a hoop of radius R and mass M rolling without slipping. Which form of kinetic energy is larger, translational or rotational? A) Translational kinetic energy is larger. B) Rotational kinetic energy is larger. C) Both are equal. D) You need to know the speed of the hoop to tell. Answer: C 12) Two balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down an incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first? A) The small sphere B) Both reach the bottom together. C) The large sphere D) It depends on the height of the incline.

3 3 13) A solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25.0e with the horizontal. What is the speed of the disk after it has rolled 3.00 m, measured along the plane? A) 3.53 m/s B) 4.07 m/s C) 5.71 m/s D) 6.29 m/s 14) A string is wrapped tightly around a fixed pulley that has a moment of inertia of kg m 2 and a radius of 12.5 cm. The string is pulled away from the pulley with a constant force of 5.00 N. As the string unwinds the pulley begins to rotate. What is the speed of the string after it has unwound 1.25 m? A) 2.09 m/s B) 2.36 m/s C) 3.18 m/s D) 4.95 m/s 15) A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her moment of inertia decreases by 1/2. Her angular speed increases by a factor of A) 2. B) 4. C) 2. D) 1/2. 16) A uniform meter stick with a mass of 135 g rotates about an axis perpendicular to the stick passing through the center of the stick with an angular speed of 3.50 rad/s 2. What is the magnitude of the angular momentum of the stick? A) kg m 2 /s B) kg m 2 /s C) kg m 2 /s D) kg m 2 /s

4 4 1. A mass (M 1 = 5.0 kg) is connected by a light cord to a mass (M 2 = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 m) rotates about a frictionless axle. The acceleration of M 2 is 3.5 m/s 2. What is the moment of inertia of the pulley? M 2 M 1 c a kg m 2 b kg m 2 c kg m 2 d kg m 2 e kg m 2 2. A wheel (radius = 0.25 m) is mounted on a frictionless, horizontal axis. The moment of inertia of the wheel about the axis is kg m 2. A light cord wrapped around the wheel supports a 0.50-kg object as shown in the figure. The object is released from rest. What is the magnitude of the acceleration of the 0.50-kg object? a. 3.0 m/s 2 b. 3.4 m/s 2 c. 4.3 m/s 2 d. 3.8 m/s 2 e. 2.7 m/s 2

5 5 c 3. Which of the following diagrams shows a non-zero net torque and a zero net force? All the rods, of length 2r, rotate about an axis that is perpendicular to the rod and fixed in the center of the rod. All the forces are of magnitude F or 2F and all distances from the axis are r or r/2. a. b. c. d. e.

6 6 d

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013 PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be