Exam 9: Rotational Motion

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

Four identical particles (mass of each = 0.24 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 centre of mass of the body and is parallel to the shorter sides of the rectangle?

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 $\degree$ below the horizontal?

Which of the following diagrams shows the greatest magnitude net torque with a zero net force? All the rods, of length 2r, rotate about an axis that is perpendicular to the rod and fixed in the centre of the rod. All the forces are of magnitude F or 2F and all distances from the axis are r or r/2.

Refer to Exhibit 9-1 below.Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track. How many revolutions does she complete in the first 12 minutes?

A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The moment of inertia of the sphere about this axis is:

A thin uniform rod (length = 1.2 m, mass = 2.0 kg) is pivoted about a horizontal, frictionless pin through one end of the rod. (The moment of inertia of the rod about this axis is ML2/3.) The rod is released when it makes an angle of 37 $\degree$ with the horizontal. What is the angular acceleration of the rod at the instant it is released?

A uniform cylinder of radius R, mass M, and length L rotates freely about a horizontal axis parallel and tangent to the cylinder, as shown below. The moment of inertia of the cylinder about this axis is

Three particles, each of which has a mass of 80 g, are positioned at the vertices of an equilateral triangle with sides of length 60 cm. The particles are connected by rods of negligible mass. What is the moment of inertia of this rigid body about an axis that is parallel to one side of the triangle and passes through the respective midpoints of the other two sides?

Refer to Exhibit 9-1 below.Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track. What is her angular displacement (in rad) in the 16-minute period shown in the graph?

A wheel rotates about a fixed axis with a constant angular acceleration of 4.0 rad/s2. The diameter of the wheel is 40 cm. What is the linear speed of a point on the rim of this wheel at an instant when that point has a total linear acceleration with a magnitude of 1.2 m/s2?

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 the horizontal position. What is the angular acceleration of the rod at the instant the rod makes an angle of 70 $\degree$ with the horizontal?

If M = 0.50 kg, L = 1.2 m, and the mass of each connecting rod shown is negligible, what is the moment of inertia about an axis perpendicular to the paper through the centre of mass? Treat the mass as particles.

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:

A particle located at the position vector m has a force N acting on it. The torque about the origin is:

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

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?

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 increases to 40 rad/s. Assume that the angular acceleration was constant during the 5.0-s interval. How many revolutions does the wheel turn through during the 5.0-s interval?

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 = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s2. At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration of a point on the rim of the wheel?