Exam 10: Rotation of a Rigid Object About a Fixed Axis

The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.

A solid sphere, a solid cylinder, a spherical shell, and a hoop all have the same mass and radius. Each are rolling on a horizontal surface with the same center of mass speed, and then they roll up identical inclines. Which one goes the greatest distance up its incline?

A solid sphere, a solid cylinder, and a hoop all have the same mass and radius. Each are sent down identical inclined planes starting from rest. Their kinetic energies at the bottom of the incline are K_sphere, K_cylinder, and K_hoop. Which of the following is true?

A uniform rod (mass = 1.5 kg) is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a horizontal position. What is the angular speed of the rod when the rod makes an angle of 30° with the horizontal? (The moment of inertia of the rod about the pin is 2.0 kg⋅m²).

The graph below shows a plot of angular acceleration in rad/s² versus time from t = 0 s to t = 8 s. The angular velocity at t = 0 s is , CCW. The angular velocity, ω, at t = 8 s is

A uniform rod (mass = 2.0 kg, length = 0.60 m) is free to rotate about a frictionless pivot at one end. The rod is released from rest in the horizontal position. What is the magnitude of the angular acceleration of the rod at the instant it is 60° below the horizontal?

Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars. If the two cars are in line at t = 0, and moving at 3ω and ω respectively, at what time will they next pass each other?

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off. The turntable comes to rest 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.

Two cylinders made of the same material roll down a plane inclined at an angle θ with the horizontal. Each travels the same distance. The radius of cylinder B is twice the radius of cylinder A. In what order do they reach the bottom?

The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-1. What is her angular displacement (in rad) in the 16 minute period shown in the graph?

Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.5 m × 4.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides?

Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the longer sides and is parallel to the shorter sides?

A uniform rod of mass M = 1.2 kg and length L = 0.80 m, lying on a frictionless horizontal plane, is free to pivot about a vertical axis through one end, as shown. The moment of inertia of the rod about this axis is given by (1/3)ML². If a force (F = 5.0 N, θ = 40°) acts as shown, what is the resulting angular acceleration about the pivot point?

A campus bird spots a member of an opposing football team in an amusement park. The football player is on a ride where he goes around at angular velocity ω at distance R from the center. The bird flies in a horizontal circle above him. Will a dropping the bird releases while flying directly above the person's head hit him?

A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure. When released from rest the object falls with a downward acceleration of 5.0 m/s². What is the moment of inertia of the wheel?

The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-1. How many revolutions does she complete in the 16 minute period?

The rigid object shown is rotated about an axis perpendicular to the paper and through point P. The total kinetic energy of the object as it rotates is equal to 1.4 J. If M = 1.3 kg and L = 0.50 m, what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles.

A horizontal force of magnitude 6.5 N is exerted tangentially on a Frisbee of mass 32 grams and radius 14.3 cm. Assuming the Frisbee, a uniform disk, is originally at rest and the force is exerted for 0.08 s, determine the angular velocity of rotation about the central axis when the Frisbee is released.

A wheel (radius = 12 cm) is mounted on a frictionless, horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel. A light cord wrapped around the wheel supports a 0.40-kg object. If released from rest with the string taut, the object is observed to fall with a downward acceleration of 3.0 m/s². What is the moment of inertia (of the wheel) about the given axle?

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s². In a 4.0-s interval the wheel turns through an angle of 80 radians. Assuming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval?