Question

A Texas cockroach of mass 0.100 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has a radius 15.1 cm, rotational inertia 4.86 x 10-3 kg·m2, and frictionless bearings. The cockroach's speed (relative to the ground) is 1.88 m/s, and the lazy Susan turns clockwise with angular velocity ω0 = 2.56 rad/s. The cockroach finds a bread crumb on the rim and, of course, stops. (a) What is the angular speed of the lazy Susan after the cockroach stops? (b) Is mechanical energy conserved as it stops?

Answer #1

A Texas cockroach of mass 0.177 kg runs counterclockwise around
the rim of a lazy Susan (a circular disk mounted on a vertical
axle) that has a radius 14.1 cm, rotational inertia 5.88 x 10-3
kg·m2, and frictionless bearings. The cockroach's speed (relative
to the ground) is 2.73 m/s, and the lazy Susan turns clockwise with
angular velocity ω0 = 3.38 rad/s. The cockroach finds a bread crumb
on the rim and, of course, stops. (a) What is the angular...

A Texas cockroach of mass 0.108 kg runs counterclockwise around
the rim of a lazy Susan (a circular disk mounted on a vertical
axle) that has a radius 12.4 cm, rotational inertia 4.19 x
10-3 kg·m2, and frictionless bearings. The
cockroach's speed (relative to the ground) is 2.81 m/s, and the
lazy Susan turns clockwise with angular velocity ω0 =
3.56 rad/s. The cockroach finds a bread crumb on the rim and, of
course, stops. (a) What is the angular...

A 50 kg woman stands at the rim of a horizontal turntable having
a moment of inertia of 560 kg·m2 and a radius of 2.0 m.
The turntable is initially at rest and is free to rotate about a
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starts walking around the rim clockwise (as viewed from above the
system) at a constant speed of 1.5 m/s relative to the Earth.
(a) In what direction and with what angular speed...

Two disks are mounted (like a merry-go-round) on low-friction
bearings on the same axle and can be brought together so that they
couple and rotate as one unit. The first disk, with rotational
inertia 3.88 kg·m2 about its central axis, is set
spinning counterclockwise (which may be taken as the positive
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7.15 kg·m2 about its central axis, is set spinning
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(a) What...

A 55.0-kg woman stands at the rim of a horizontal turntable
having a moment of inertia of 420 kg · m2 and a radius of 2.00 m.
The turntable is initially at rest and is free to rotate about a
frictionless vertical axle through its center. The woman then
starts walking around the rim clockwise (as viewed from above the
system) at a constant speed of 1.50 m/s relative to the Earth. (a)
In what direction does the turntable rotate?...

A 65.0-kg woman stands at the rim of a horizontal turntable
having a moment of inertia of 460 kg · m2 and a radius of 2.00 m.
The turntable is initially at rest and is free to rotate about a
frictionless vertical axle through its center. The woman then
starts walking around the rim clockwise (as viewed from above the
system) at a constant speed of 1.50 m/s relative to the Earth.
(a) In what direction does the turntable rotate?...

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