Exam 12: Rotation I: Kinematics and Dynamics

Exhibit 12-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. ​ ​ Use this exhibit to answer the following question(s). -Refer to Exhibit 12-2. What is his average angular acceleration, in rad/s², in the first 10 minutes?

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?

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. Relative to the positive direction of the axis of rotation, the angular positions of the sphere are negative, its angular velocity is negative, and its angular acceleration is positive. The sphere is

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 wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² starts from rest at t = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?

A rigid rod of length l rotates about an axis perpendicular to the rod, with one end of the rod fixed to the axis. Which of the following are equal at all points on the rod? I.The angular position II.The angular velocity III.The angular acceleration IV.The centripetal acceleration V.The tangential acceleration

Two vectors lying in the xz plane are given by the equations and . The value of is

Two forces of magnitude 50 N, as shown in the figure below, act on a cylinder of radius 4 m and mass 6.25 kg. The cylinder, which is initially at rest, sits on a frictionless surface. After 1 second, the velocity and angular velocity of the cylinder in m/s and rad/s are respectively

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² turns through 2.4 revolutions during a 2.0-s time interval. What is the angular velocity at the end of this time interval?

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 rotational 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? ​ ​

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). -What is her angular displacement (in rad) in the first 8 minutes?

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 small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. Relative to the positive direction of the axis of rotation, the angular positions of the sphere are positive, its angular velocity is positive, and its angular acceleration is negative. The sphere is

The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. ​ ​ Use this exhibit to answer the following question(s). -The angular position, θ, at t = 0 s is 3.0 rad, clockwise. The angular position, θ, at t = 7 s is

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular acceleration of the rod at the instant it is released?

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes?

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval?

Particles (mass of each = 0.40 kg) are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot?

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?

A wheel (radius = 0.25 m) is mounted on a frictionless, horizontal axis. The rotational inertia of the wheel about the axis is 0.040 kg⋅m². 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? ​ ​