Exam 10: Energy and Momentum in Rotating Systems

A regulation basketball has a 25.0-cm diameter and a mass of 0.560 kg. It may be approximated as a thin spherical shell with a moment of inertia $\frac{2}{3}$ MR2. Starting from rest, how long will it take a basketball to roll without slipping 4.00 m down an incline at 30.0 $\degree$ to the horizontal?

A hockey puck travelling at speed v on essentially frictionless ice collides elastically with one end of a straight stick lying flat on the ice. In this collision:

The object shown below has mass m and velocity . The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is:

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5. What is its angular momentum (in kg.m²/s) relative to the origin?

A torque can be exerted on a body with a fixed axis of rotation:

A uniform rod is 3.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 27 $\degree$ above the horizontal. What is the angular speed of the rod as it passes through the horizontal position?

A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its centre, what is the final angular velocity (in rad/s) of the system after the collision?

During a race on the Gold Coast, a car of mass 1000 kg moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its angular momentum (in kg.m²/s) relative to the centre of the racetrack?

A coin with a diameter 3.00 cm rolls up a 30.0 $\degree$ inclined plane. The coin starts out with an initial angular speed of 60.0 rad/s and rolls in a straight line without slipping. If the moment of inertia of the coin is $\frac{1}{2}$ MR2, how far will the coin roll up the inclined plane?

A top is set spinning so that the rotation is counterclockwise around its axis when viewed from above. When the top is placed on a level surface it happens that its axis of rotation is not quite vertical. Viewed from above, which way does the rotational axis of the top precess?

A non-uniform 2.0-kg rod is 2.0 m long. The rod is mounted to rotate freely about a horizontal axis perpendicular to the rod that passes through one end of the rod. The moment of inertia of the rod about this axis is 4.0 kg.m². The centre of mass of the rod is 1.2 m from the axis. If the rod is released from rest in the horizontal position, what is its angular speed as it swings through the vertical position?

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s along the direction . What is its angular momentum (in kg.m²/s) relative to the origin?

A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is:

The net work done in accelerating a propeller from rest to an angular velocity of 200 rad/s is 3000 J. What is the moment of inertia of the propeller?

Two objects of mass m1 = 2m and m² = m move around a rotation axis A in parallel circles of radii r1 = r and r2 = 2r with equal tangential speeds. As they rotate, forces of equal magnitude are applied opposite to their velocities to stop them. Which statement is correct?

A pendulum bob of mass m is set into motion in a circular path in a horizontal plane as shown in the figure. The square of the angular momentum of the bob about the vertical axis through the point P is:

The diagram below shows five 20-kg rods of the same 2.0-m length free to rotate about axes through the rods, as indicated. Which rod experiences the greatest magnitude gravitational torque?

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 centre of mass speed, and then they roll up identical inclines. Which one goes the greatest distance up its incline?

Two cylinders made of the same material roll down a plane inclined at an angle $\theta$ 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?

If L represents angular momentum, I represents moment of inertia, p represents linear momentum, m represents mass, and r represents a distance, which of the following can represent kinetic energy?