Exam 11: Rolling, Torque, and Angular Momentum

A simple gyroscope consists of a wheel (R = 0.75 m, I = 0.9 MR²)rotating on a horizontal shaft.If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel?

A thin-walled hollow tube rolls without sliding along the floor.The ratio of its translational kinetic energy to its rotational kinetic energy (about an axis through its center of mass)is:

A solid sphere and a solid cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane sliding down the incline.Then:

The fundamental dimensions of angular momentum are:

As a 2.0-kg block travels around a 0.50-m radius circle it has an angular speed of 12 rad/s.The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin.The magnitude of its angular momentum around the origin is:

The coefficient of static friction between a certain cylinder and a horizontal floor is 0.40.If the rotational inertia of the cylinder about its symmetry axis is given by I = (1/2)MR², then the maximum acceleration the cylinder can have without sliding is:

A 2.0-kg stone is tied to a 0.50-m long string and swung around a circle at a constant angular velocity of 12 rad/s.The net torque on the stone about the center of the circle is:

The newton.second is a unit of:

A phonograph record is dropped onto a freely spinning turntable.Then:

A pulley with radius R and rotational inertia I is free to rotate on a horizontal fixed axis through its center.A string passes over the pulley.A block of mass m₁ is attached to one end and a block of mass m_2, is attached to the other.At one time the block with mass m₁ is moving downward with speed v.If the string does not slip on the pulley, the magnitude of the total angular momentum, about the pulley center, of the blocks and pulley, considered as a system, is given by:

A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter has an acceleration given by in m/s².The torque, relative to the origin, acting on it at the end of 2.0 s is:

When a wheel rolls without slipping,

Two pendulum bobs of unequal mass are suspended from the same fixed point by strings of equal length.The lighter bob is drawn aside and then released so that it collides with the other bob on reaching the vertical position.The collision is elastic.What quantities are conserved in the collision?

A man, with his arms at his sides, is spinning on a light frictionless turntable.When he extends his arms:

A pulley with radius R is free to rotate on a horizontal fixed axis through its center.A string passes over the pulley.Mass m₁ is attached to one end and mass m₂ is attached to the other.The portion of the string attached to m₁ has tension T₁ and the portion attached to m₂ has tension T₂.The magnitude of the total external torque, about the pulley center, acting on the masses and pulley, considered as a system, is given by:

A 6.0-kg particle moves to the right at 4.0 m/s as shown.The magnitude of its angular momentum about the point O is:

A particle moves along the x axis.In order to calculate the torque on the particle, you need to know:

The angular momentum vector of Earth, due to its daily rotation, is directed:

A playground merry-go-round has a radius R and a rotational inertia I.When the merry-go-round is at rest, a child with mass m runs with speed v along a line tangent to the rim and jumps on.The angular velocity of the merry-go-round is then:

A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating turntable.The effect of the weights is to double the rotational inertia of the system.As he is rotating, the man opens his hands and drops the two weights.They fall outside the turntable.Then: