Question

The pendulum in the figure consists of a uniform disk with radius r = 11.0 cm and mass 470 g attached to a uniform rod with length L = 640 mm and mass 240 g. (a) Calculate the rotational inertia of the pendulum about the pivot point. (b) What is the distance between the pivot point and the center of mass of the pendulum? (c) Calculate the period of oscillation

Answer #1

The pendulum in the figure consists of a uniform disk with
radius r = 13.0 cm and mass 880 g attached to a uniform
rod with length L = 610 mm and mass 290 g.
(a)Calculate the rotational inertia of the
pendulum about the pivot point. (b) What is the
distance between the pivot point and the center of mass of the
pendulum? (c)Calculate the period of
oscillation.

In the figure, a small disk of radius r=1.00 cm has been glued
to the edge of a larger disk of radius R=6.00 cm so that the disks
lie in the same plane. The disks can be rotated around a
perpendicular axis through point O at the center of the larger
disk. The disks both have a uniform density (mass per unit volume)
of 1.40 × 103 kg/m3 and a uniform thickness of 7.00 mm. What is the
rotational inertia...

In the figure, a small disk of radius r=2.00 cm has
been glued to the edge of a larger disk of radius R=7.00
cm so that the disks lie in the same plane. The disks can be
rotated around a perpendicular axis through point O at the
center of the larger disk. The disks both have a uniform density
(mass per unit volume) of 1.40 × 10^3 kg/m3 and a
uniform thickness of 6.00 mm. What is the rotational inertia...

A grandfather clock has a pendulum that consists of a thin brass
disk of radius 21 cm and mass 1 kg that is attached to a long, thin
rod of negligible mass. The pendulum swings freely about an axis
perpendicular to the rod and through the end of the rod opposite
the disk. The pendulum should be designed so that its period is 2 s
for small oscillations when the gravitational acceleration is 9.8
m/s2.
(a) What should the length...

A grandfather clock has a pendulum that consists of a thin brass
disk of radius 25 cm and mass 1.9 kg that is attached to a long,
thin rod of negligible mass. The pendulum swings freely about an
axis perpendicular to the rod and through the end of the rod
opposite the disk. The pendulum should be designed so that its
period is 2 s for small oscillations when the gravitational
acceleration is 9.8 m/s2.
(a) What should the length...

A system consists of a point mass
m=0.76kg and a uniform solid cylinder of
mass Mcylinder=2.15kg and
radius R=0.43m attached to both ends of a
uniform rigid rod of mass
Mrod=2.15kg and length
L=2.71m, as shown in the ﬁgure. The
system is free to rotate about the y axis, which is at a distance x
away from the point mass. The y axis is parallel to the side of the
cylinder and perpendicular to the length of the rod. Find...

THE BUBBLE MOMENT
A physical pendulum is composed a rod of length 26 cm and radius
3.2 cm suspended downward from one of its ends. At the bottom, free
end, there is a large, circular bubble of the same radius as the
rod so that it is wholly within the rod, but as far towards the
bottom as possible.
(a) If the rod has a density of 9 g/cm3, what is its
mass?
(b) Find its center of mass if...

The assembly shown in the figure below consists of a thin rod of
length
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
initially vertical and at rest when it starts to rotate
clockwise.
A thin rod of length ℓ...

In the figure the lower disk, of mass 440 g and radius 3.7 cm ,
is rotating at 180 rpm on a frictionless shaft of negligible
radius. The upper disk, of mass 280 g and radius 2.0 cm , is
initially not rotating. It drops freely down onto the lower disk,
and frictional forces bring the two disks to a common rotational
speed. A) Find the common speed. B) Find the fraction of the
initial kinetic energy lost to friction.

A uniform plank of mass 2.53 kg and length 21.5 cm is pivoted at
one end. A spring of force constant 403 N/m is attached to the
center of the plank, as shown in the figure. The height of the
pivot has been adjusted so that the plank will be in equilibrium
when it is horizontally oriented.
Find the period of small oscillation about the equilibrium
point. Answer in units of s.

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