Question

A pulley of mass ? and radius ? (? = 1 2 ?? 2 ) is free to rotate around its fixed axis without friction. A spider of mass ? falls vertically (starting with zero initial velocity) from a point on the ceiling which is a height ℎ above and a distance ? to the right of the center of the pulley (Figure on the left). The spider holds on to the pulley as soon as it hits, and the pulley and the spider start rotating. Gravitational acceleration is g. (a) (5 Pts.) What is the speed of the spider just before it hits the pulley? (b) (5 Pts.) What is the angular speed of the pulley with the spider on it just after the collision? (c) (5 Pts.) Find the angular velocity of the pulley at the time the spider reaches the bottom of the pulley. (d) (5 Pts.) How much energy is lost during the collision?

Answer #1

A thin, uniform, 15.5 kg post, 2.35 m long, is held vertically
using a cable and is attached to a 5.00-kg mass and a pivot at its
bottom end (the figure (Figure 1)). The string attached to the
5.00-kg mass passes over a massless, frictionless pulley and pulls
perpendicular to the post. Suddenly the cable breaks.
A) Find the angular acceleration of the post about the pivot
just after the cable breaks.
B)Will the angular acceleration in part (A) remain...

A turntable has a radius R and mass M (considered as a disk) and
is rotating at an angular velocity w0 about a frictionless vertical
axis. A piece of clay is tossed onto the turntable and sticks d
from the rotational axis. The clay hits with horizontal velocity
component vc at right angle to the turntable’s radius, and in a
direction that opposes the rotation. After the clay lands, the
turntable has slowed to angular velocity w1. A) Find the...

A turntable has a radius R and mass M (considered as a disk) and
is rotating at an angular velocity W0 about a frictionless vertical
axis. A piece of clay is tossed onto the turntable and sticks d
from the rotational axis. The clay hits with horizontal velocity
component vc at right angle to the turntable’s radius, and in a
direction that opposes the rotation. After the clay lands, the
turntable has slowed to angular velocity W1. A) Find the...

Two Balls and a Thin Rod
Two balls of mass 2.43 kg are attached to the ends of a
thin rod of negligible mass and length 60 cm. The rod is
free to rotate without friction about a horizontal axis through its
center. A putty wad of mass 126 gdrops onto one of the
balls, with a speed 2.6 m/s, and sticks to it.
What is the angular speed of the system just after the putty wad
hits?
What is...

A bowling ball (solid sphere, moment of inertia is
(2/5)MR2) of mass M and radius R rolls down a hill
without slipping for a distance of L along the hill with slope of
angle θ, starting from rest. At that point, the hill becomes
frictionless.The ball continues down the hill for another segment
of length 2L (thus the total distance travelled on the hill is 3L).
The hill levels out into a horizontal area, where the coefficient
of friction is...

A playground ride consists of a disk of mass M = 59 kg
and radius R = 1.9 m mounted on a low-friction axle. A
child of mass m = 18 kg runs at speed v = 2.2 m/s
on a line tangential to the disk and jumps onto the outer edge of
the disk.
(b) Relative to the axle, what was the magnitude of the angular
momentum of the child before the collision?
L|C| =
(c) Relative to the...

A hanging weight, with a mass of m1 = 0.355
kg, is attached by a rope to a block with mass
m2 = 0.845 kg as shown in the figure below. The
rope goes over a pulley with a mass of M = 0.350 kg. The
pulley can be modeled as a hollow cylinder with an inner radius of
R1 = 0.0200 m, and an outer radius of
R2 = 0.0300 m; the mass of the spokes is
negligible. As...

1. A railroad car of mass 2.40E+4 kg moving with a speed of 3.10
m/s collides and couples with two other coupled railroad cars each
of the same mass that are already moving in the same direction at a
speed of 1.00 m/s.
a. What is the speed (in m/s) of the three coupled cars after
the collision?
b.How much kinetic energy (in J) is lost in the collision?
2.A ring (2 kg, r = 2 m) rotates in a...

Two Balls and a Thin Rod
Two balls of mass 3.29 kg are attached to the ends of a
thin rod of negligible mass and length 72 cm. The rod is
free to rotate without friction about a horizontal axis through its
center. A putty wad of mass 127 g drops onto one of the
balls, with a speed 2.5 m/s, and sticks to it.
What is the angular speed of the system just after the putty wad
hits?
1.31×10-1...

A cylindrical rod of length 2.0 m, radius 0.5 m, and mass 1.5 kg
has two spheres attached on its ends. The centers of the spheres
are 1.0 m from the center of the rod. The mass of each sphere is
0.66 kg. The rod is capable of rotating about an axis passing
through its center and perpendicular to the plane of the page, but
the set up is stationary to begin with. A small mass of value 0.19
kgmoving...

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