Rotational Kinematics & Torque MC Practice...

Rotational Kinematics & Torque MC Question Database

(Questions #22,31,32,33 each have TWO correct answers.)

1) Why must radians be used in rotational motion problems? a) Because radians are the unit of displacement b) Because radians are based on the properties of a circle, unlike degrees c) Because radians make the numbers come out correctly d) Because radians are based on the properties of rotation, unlike degrees e) Radians are an alternative to degrees; either can be used 2) The hour hand in a clock makes two revolutions in 24 hours while the minute hand makes one revolution each hour. What are the angular velocities (in radians/sec) of the hour hand and minute hand, respectively?

a) 1 and 1/12 b) 2π and π/6 c) π/1,800 and π/30 d) π/21,600 and π/1,800 e) 3,600 and 60


3) A boy and girl are on a rotating merry-go-round. The girl is on the outer edge, while the boy is halfway between the center and the girl. How does the rotational speed of the girl compare to that of the boy? a) The girl’s rotational speed is four times as much. b) The girl’s rotational speed is twice as much. c) The girl’s rotational speed is the same. d) The girl’s rotational speed is half as much. e) The girl’s rotational speed is one-fourth as much. 4) A boy and girl are on a rotating merry-go-round. The girl is on the outer edge, while the boy is halfway between the center and the girl. How does the linear speed of the girl compare to that of the boy? a) The girl’s linear speed is four times as much. b) The girl’s linear speed is twice as much. c) The girl’s linear speed is the same. d) The girl’s linear speed is half as much. e) The girl’s linear speed is one-fourth as much.


5) An object is rotating at a constant angular velocity of 0.5 rad/s. What angle does the object rotate through is 12 s?

a) 0.1° b) 30° c) 180° d) 340° e) 2,160°

6) A propeller, initially at rest, rotates about its midpoint with an angular acceleration of 12 rad/s2. How much time will it take to rotate through a 90° angle?

a) 0.51 s b) 0.72 s c) 1.2 s d) 3.9 s e) 4.1 s


7) A car tire is initially spinning with an angular speed of 150 rad/s. As the brakes are applied, the tire slows down at a rate of 25 rad/s2. How long does it take the car to stop?

a) 2.0 s b) 2.5 s c) 3.0 s d) 5.0 s e) 6.0 s 8) Starting from rest, a spinning disk accelerates constantly to a final rotational speed, ω, in a period of time, Δt. What expression best represents the revolutions the disk has turned through? a) ωΔt/2π b) ωΔt/4π c) ωΔt2/2 d) ω/Δt e) 2πωΔt


9) A baton of length L rotates with a constant angular velocity, ω, measured in radians per second. What is the period of the beam’s rotation? a) 2πL/ω b) ω/2π c) 1/ω d) 2π/ω e) ω/2πL 10) A disk, initially rotating at 11 rad/s, slows down at a constant rate of 1.5 rad/s2. What is the angular displacement of the disk in 6 s of time? a) 9 rad b) 27 rad c) 39 rad d) 66 rad e) 93 rad


11) A 45 kg girl is sitting on a see-saw 0.6 m from the balance point, as shown below. How far, on the other side, should a 60 kg boy sit so the see-saw will remain in balance?

a) 0.30 m b) 0.35 m c) 0.40 m d) 0.45 m e) 0.50 m 12) Two children make a seesaw out of a 5 m wooden plank. They balance it on a fulcrum located 2 m from the left end. The 42 kg child sits at the end of the plank on the left side. What distance (measured from the fulcrum) can the 35 kg child sit on the right side of the plank to keep it balanced?

a) 1.0 m b) 1.5 m c) 2.0 m d) 2.4 m e) 3.0 m


13) A uniform meter stick of mass 1 kg is hanging from a thread attached at the stick’s midpoint. One block of mass m = 3 kg hangs from the left end of the stick, and another block, of unknown mass M, hangs below the 80 cm mark on the meter stick. If the stick remains rest in the horizontal position shown above, what is M? a) 4 kg b) 5 kg c) 6 kg d) 8 kg


14) A 10 kg uniform plank of length L is pivoted at its center. A 4 kg mass is to be placed on the right end. How far from the pivot must a 6 kg mass be placed to keep the plank in equilibrium? a) L/2 b) L/4 c) 3L/4 d) L/3 e) 2L/3


15) A balanced meter stick is shown below. The distance from the fulcrum is shown for each mass except the 10 g mass. What is the approximate position of the 10 g mass, based on the diagram?

a) 7 cm b) 9 cm c) 10 cm d) 15 cm e) 21 cm

40 cm 40 cm

20 cm

5 cm X

50 g 10 g 20 g 40 g 30 g


16) Newton’s first law states that a point particle is in equilibrium if the net forces acting on it are zero. When are torques considered in Newton’s first law? a) Torques are never included in Newton’s first law. b) When the forces are unbalanced c) When considering objects that have dimensions d) Torques are not forces and do not need to be accounted for. e) Torques come in pairs and do not need to be accounted for. 17) What happens to an object on which a net torque is acting? a) Nothing happens to it. b) It causes the object to accelerate linearly. c) It causes the object to experience linear and angular acceleration. d) It causes the object to experience linear and angular acceleration. e) It causes the object to decelerate linearly.


18) What defines a lever arm? a) The distance parallel to the line of action of the force b) The distance parallel to the line of action of the force from the pivot point c) The length of the lever d) The perpendicular distance from the pivot to the line of action of the force e) F = |F| cos (θ)x


19) In an effort to tighten a bolt, a force F is applied as shown in the figure above. If the distance from the end of the wrench to the center of the bolt is 20 cm and F = 20 N, what is the magnitude of the torque produced by F? a) 1 Nm b) 2 Nm c) 4 Nm d) 10 Nm


20) A 1 m pry bar is held horizontally and used to open a crate. The tip of the bar, which serves as the fulcrum, is pushed a distance of 2 cm between the crate lid and the crate. If a 20 N force is applied perpendicularly to the end of the bar, what force is applied on the crate lid?

a) 1 N b) 98 N c) 9.80 N d) 980 N e) 9,800 N 21) A 2 m long lever is held horizontally with the fulcrum placed at 0.5 m from the left end. How much vertical force must be applied to the right end of the lever to support a 1000 N rock on the left end?

a) 67 N b) 670 N c) 330 N d) 1,000 N e) 22 N


22) A torque is applied about the axis of rotation in which of the following scenarios?

a) A force is applied parallel to the lever arm and through the axis of rotation. b) A force is applied perpendicular to the lever arm and through the axis of rotation. c) A force is applied perpendicular to the lever arm but not through the axis of rotation. d) A force is applied at a 45° angle but not through the axis of rotation. e) A force is applied at a 45° angle through the axis of rotation.


23) Four identical rods shown below experience the forces as shown. Rank the magnitude of the torques about the pivot point on the left end of the rod.

a) III > I = IV > II b) II > IV > III > I c) I = III = IV > II d) III > II > I > IV e) II = III > I > IV


24) A solid cylinder consisting of an outer radius R1 and an inner radius R2 is pivoted on a frictionless axle as shown below. A string is wound around the outer radius and is pulled to the right with a force F1 = 3 m. A second string is wound around the inner radius and is pulled down with a force F2 = 5 N. If R1 = 0.75 m and R2 = 0.35 m, what is the net torque acting on the cylinder?

a) 2.25 Nm b) -2.25 Nm c) 0.5 Nm d) -0.5 Nm e) 0 Nm


Answer questions 25 and 26 based on the following diagram, in which the rod is considered massless.

25) What is the net torque about an axis through point A? a) 16.5 Nm b) 15.2 Nm c) -5.5 Nm d) -7.8 Nm e) 6 Nm 26) What is the net torque about an axis through point C? a) 3.5 Nm b) 7.5 Nm c) -15.2 Nm d) 5.9 Nm e) 7 Nm


27) In the figure above, what is the torque produced by the bob about the pendulum’s suspension point, given that the length of the pendulum, L is 80 cm and m = 0.5 kg? a) 0.5 Nm b) 1.0 Nm c) 1.7 Nm d) 2.0 Nm


28) A cylinder is rotating clockwise about a frictionless axle when two forces are applied to the rim of the cylinder as shown below.

As a result, the cylinder will rotate with

a) increasing angular speed in the clockwise direction since |F1| > |F2| b) decreasing angular speed in the clockwise direction since the net force acting on the cylinder is |Fnet| = |F1| - |F2| c) decreasing angular speed in the clockwise direction since |τ1| > |τ2| d) increasing angular speed in the clockwise direction since |τ1| > |τ2|


29) Various forces are applied to 4 identical rods as show below. Rank the forces from the one that causes the greatest change in angular velocity to the one that causes the least.

a) II > IV > I > III b) IV > II > I > III c) II > I > IV > III d) I > II > IV > III


30) Various forces are exerted on 4 identical cylinders as shown. Rank the cylinders from the one whose angular velocity undergoes the greatest change to the one that undergoes the least.

a) D > A > C > B b) D > A = C > B c) B > C > A > D d) A = C > D > B 31) What is moment of inertia? a) The resistance something has to rotational motion b) The resistance an object has to linear motion c) The integral of volume d) The rotational equivalent of momentum e) The ratio between torque and angular acceleration


32) When a solid object rotates with a constant angular acceleration, which of the following are true? a) The net torque on the object is zero. b) The net torque on the object is constant and non-zero. c) The net torque on the object must increase. d) The object’s angular velocity changes at a steady rate. e) The object’s angular velocity is constant. 33) The moment of inertia of a body does NOT depend on which of the following? a) The angular acceleration of the body b) The distribution of mass in the body c) The angular velocity of the body d) The axis of rotation of the body e) The mass of the body


34) A cylinder has a moment of inertia, I. How much time does it take a torque, τ, to increase its angular speed from ω1 to ω2? a) (Iω2 – Iω1)/τ b) τ/(Iω1 - Iω2) c) (Iω1 - Iω2)τ d) τ/(½Iω1

2 - ½Iω22)

e) (½Iω12 - ½Iω2

2)τ

35) An object, initially rotating with an angular speed of 1.5 rad/s, is subjected to a torque of 55 Nm that accelerates it constantly at 5 rad/s2. What is the object’s moment of inertia? a) 3.0 kgm2 b) 3.5 kgm2 c) 5.5 kgm2 d) 11 kgm2 e) 50 kgm2


36) A pulley has a radius of 45 cm and a moment of inertia of 0.15 kgm2. A string is wrapped around the pulley, and a 25 g mass is hung from the string on one side of the pulley. Calculate the magnitude of the angular acceleration of the pulley. a) 0.075 rad/s2 b) 0.15 rad/s2 c) 0.74 rad/s2 d) 1.6 rad/s2 e) 3.3 rad/s2 37) The crane is used to pick up a 50 m long steel beam to place in a building. The beam is uniform, but the crane cable is placed 2 m off the center of the beam. How much vertical force must be placed on the guide rope to keep the beam level? The beam has a mass of 5 kg/m, and the guide rope is placed on the end on the end of the shorter side of the beam.

a) 210 N b) 210 kg c) 21 N d) 21 kg e) 110 N


38) A four-wheeled, 5 kg baby carriage carries a 5 kg baby. The front wheels are 60 cm from the back wheels and 90 cm from the carriage handle. Assuming that the center of gravity for the baby and the carriage’s center is equidistant between the front and back wheels, what force must the mother apply to tip the carriage back the carriage back to lift the front wheels?

a) 10 kg b) 100 N c) 5 kg d) 50 N e) 1 kg

Rotational Kinematics & Torque MC Practice...

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