Exam 11: Rolling, Torque, and Angular Momentum

A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center.Assume the hoop is connected to the rotation axis by light spokes.With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown.Rank the objects according to their angular momenta after a given time t, least to greatest.

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 simple gyroscope consists of a wheel (M = 2.0 kg, R = 0.75 m, I = 1.1 kg∙m²)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 wheel, with rotational inertia I, mounted on a vertical shaft with negligible rotational inertia, is rotating with angular speed $\omega$ _0.A nonrotating wheel with rotational inertia 2I is suddenly dropped onto the same shaft as shown.The resultant combination of the two wheels and shaft will rotate at:

A 2.0-kg block travels around a 0.50-m radius circle with an angular velocity of 12 rad/s.The magnitude of its angular momentum about the center of the circle is:

Two wheels roll side-by-side without sliding, at the same speed.The radius of wheel 2 is twice the radius of wheel 1.The angular velocity of wheel 2 is:

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:

Possible units of angular momentum are:

A 2.0-kg block travels around a 0.50-m radius circle with an angular speed of 12 rad/s.The circle is parallel to the xy plane and is centered on the z axis, a distance of 0.75 m from the origin.The z component of the angular momentum around the origin 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 circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin.The magnitude of the torque about the origin is:

Two uniform cylinders have different masses and different rotational inertias.They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane.The cylinder that gets to the bottom first is:

A block with mass M, on the end of a string, moves in a circle on a horizontal frictionless table as shown.As the string is slowly pulled through a small hole in the table:

When a man on a frictionless rotating stool extends his arms horizontally, his rotational kinetic energy:

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

The fundamental dimensions of angular momentum are:

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 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:

Two identical disks, with rotational inertia I (= 1/2 MR²), roll without slipping across a horizontal floor and then up inclines.Disk A rolls up its incline without sliding.On the other hand, disk B rolls up a frictionless incline.Otherwise the inclines are identical.Disk A reaches a height 12 cm above the floor before rolling down again.Disk B reaches a height above the floor of:

A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg∙m².It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim.When the child reaches the rim the angular velocity of the merry-go-round is:

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: