Question

The figure shows a rigid assembly of a thin hoop (of mass m = 0.14 kg and radius R = 0.11 m) and a thin radial rod (of length L = 2R and also of mass m = 0.14 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?

Answer #1

The figure shows a rigid assembly of a thin hoop (of mass m =
0.23 kg and radius R = 0.16 m) and a thin radial rod (of length L =
2R and also of mass m = 0.23 kg). The assembly is upright, but we
nudge it so that it rotates around a horizontal axis in the plane
of the rod and hoop, through the lower end of the rod. Assuming
that the energy given to the assembly in...

The assembly shown in the figure below consists of a thin rod of
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ℓ = 23.2 cm
and mass
m = 1.20 kg
with a solid sphere of diameter
d = 10.0 cm
and mass
M = 2.00 kg
attached to its top. The assembly is free to pivot about a
frictionless axle through the bottom of the rod. The assembly is
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clockwise.
A thin rod of length ℓ...

A rigid rod of mass 5.30 kg and length of 1.50 m rotates in a
vertical (x,y) plane about a frictionless pivot through its center.
Particles m_1 (mass=6.30 kg) and m_2 (mass=2.20 kg) are attached at
the ends of the rod. Determine the size of the angular acceleration
of the system when the rod makes an angle of 42.1° with the
horizontal.

A uniform thin rod of length 0.56 m and mass 3.2 kg can rotate
in a horizontal plane about a vertical axis through its center. The
rod is at rest when a 3.5 g bullet traveling in the rotation plane
is fired into one end of the rod. As viewed from above, the
bullet's path makes angle θ = 60° with the rod. If the
bullet lodges in the rod and the angular velocity of the rod is
12.0 rad/s...

A thin, cylindrical rod ℓ = 27.0 cm long with a mass m = 1.20 kg
has a ball of diameter d = 10.00 cm and mass M = 2.00 kg attached
to one end. The arrangement is originally vertical and stationary,
with the ball at the top as shown in the figure below. The
combination is free to pivot about the bottom end of the rod after
being given a slight nudge.
(a) After the combination rotates through 90...

In the figure, two particles, each with mass m = 0.86
kg, are fastened to each other, and to a rotation axis at
O, by two thin rods, each with length d = 5.4 cm
and mass M = 1.2 kg. The combination rotates around the
rotation axis with angular speed ω = 0.33 rad/s. Measured
about O, what is the combination's (a)
rotational inertia and (b) kinetic energy?

A thin, rigid, uniform rod has a mass of 1.40 kg and a length of
2.50 m. (a) Find the moment of inertia of the rod relative to an
axis that is perpendicular to the rod at one end. (b) Suppose all
the mass of the rod were located at a single point. Determine the
perpendicular distance of this point from the axis in part (a),
such that this point particle has the same moment of inertia as the
rod...

A uniform thin rod of length 0.45 m and mass 6.5 kg can rotate
in a horizontal plane about a vertical axis through its center. The
rod is a rest when a 3.0-g bullet traveling in the horizontal plane
of the rod is fired into one end of the rod. As viewed from above,
the direction of the bullet velocity makes an angle of 60° with the
rod (see the figure). If the bullet lodges in the rod and 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.
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What is...

The uniform thin rod in the figure below has mass M =
2.00 kg and length L = 2.87 m and is free to rotate on a
frictionless pin. At the instant the rod is released from rest in
the horizontal position, find the magnitude of the rod's angular
acceleration, the tangential acceleration of the rod's center of
mass, and the tangential acceleration of the rod's free end.
HINT
An illustration shows the horizontal initial position and
vertical final position...

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