A grandfather clock contains a pendulum that swings back and
forth due to gravity. Model the pendulum as a one-dimensional rod
that is connected to a solid disk. The length of the rod is
L, and the radius of the solid disk is R. The
mass of each object is 
.
Known: ,
L, R, g
What is the angular acceleration of the
swinging pendulum when it is at an angle 
relative to the vertical, as shown? Let counterclockwise be the
positive direction. Write the answer only in terms of the known
quantities and fully simplify the answers.
Homework Answers
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A grandfather clock contains a pendulum that swings back and
forth due to gravity. Model the...
A pendulum swings back and forth. The pendulum is a one-dimensional rod that is connected to...
A pendulum swings back and forth. The pendulum is a one-dimensional rod that is connected to a disk. The length of the rod is L and the radius of the disk is R. The mass of each object is M0. At this point, we know: M0, L, R, and g Part A: What is the angular acceleration of the swinging pendulum when it at angle θ relative to vertical? Counterclockwise is the positive direction. Answer in known quantities and simplify...
A pendulum swings back and forth. The pendulum is a one-dimensional rod that is connected to...
A pendulum swings back and forth. The pendulum is a one-dimensional rod that is connected to a disk. The length of the rod is L and the radius of the disk is R. The mass of each object is M0. At this point, we know: M0, L, R, and g Part A: What is the angular acceleration of the swinging pendulum when it at angle θ relative to vertical? Counterclockwise is the positive direction. Answer in known quantities and simplify...
A grandfather clock has a pendulum that consists of a thin brass disk of radius 37...
A grandfather clock has a pendulum that consists of a thin brass
disk of radius 37 cm and mass 1.6 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 r...
A grandfather clock has a pendulum that consists of a thin brass disk of radius r = 14.38 cm and mass 0.8261 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, as shown in the figure. If the pendulum is to have a period of 1.592 s for small oscillations at a place where g =...
A grandfather clock has a pendulum that consists of a thin brass disk of radius 27...
A grandfather clock has a pendulum that consists of a thin brass
disk of radius 27 cm and mass 1.1 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 40...
A grandfather clock has a pendulum that consists of a thin brass disk of radius 40 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...
You are visiting your grandparents in Boston. There is an antique grandfather clock keeping time in...
You are visiting your grandparents in Boston. There is an antique grandfather clock keeping time in one of the rooms. Your grandmother enters the room and tells you that she had it calibrated professionally in Denver and it kept perfect time for years. After they moved it here to their Massachusetts house, it has not been accurate. It runs too fast and has to be reset to the correct time every few days. You find some papers associated with the...
You are visiting your grandparents in Boston. There is an antique grandfather clock keeping time in...
You are visiting your grandparents in Boston. There is an antique grandfather clock keeping time in one of the rooms. Your grandmother enters the room and tells you that she had it calibrated professionally in Denver and it kept perfect time for years. After they moved it here to their Massachusetts house, it has not been accurate. It runs too fast and has to be reset to the correct time every few days. You find some papers associated with the...
3) A pendulum consists of a solid spherical mass of mass 3m and radius R whose...
3) A pendulum consists of a solid spherical mass of mass 3m and radius R whose center is attached to the end of a uniform rod of mass m and length 4R which is pivoted about an axis at its end. a) The pendulum is constructed with a sphere of mass 1.5 kg and radius 15 cm, rod of mass .50 kg and length 60 cm. The mass swings in simple harmonic motion of maximum amplitude of /6 radians. Find...
5*) Find the angular velocity of the Earth due to its daily rotation and express it...
5*) Find the angular velocity of the Earth due to its daily
rotation and express it in radians per second. Then use it, and a
model of the Earth as a solid sphere of mass M=
5.97 × 1024 kg and radius R
= 6.37 × 106 m, to estimate the angular momentum of the Earth due
to its rotation around its axis. (The result should be of the order
of 1033 kg m2/s. This is called the Earth’s “intrinsic”...
A grandfather clock has a pendulum that consists of a thin brass
disk of radius 37 cm and mass 1.6 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 r = 14.38 cm and mass 0.8261 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, as shown in the figure. If the pendulum is to have a period of 1.592 s for small oscillations at a place where g =...
A grandfather clock has a pendulum that consists of a thin brass
disk of radius 27 cm and mass 1.1 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...
You are visiting your grandparents in Boston. There is an antique grandfather clock keeping time in one of the rooms. Your grandmother enters the room and tells you that she had it calibrated professionally in Denver and it kept perfect time for years. After they moved it here to their Massachusetts house, it has not been accurate. It runs too fast and has to be reset to the correct time every few days. You find some papers associated with the...
3) A pendulum consists of a solid spherical mass of mass 3m and radius R whose center is attached to the end of a uniform rod of mass m and length 4R which is pivoted about an axis at its end. a) The pendulum is constructed with a sphere of mass 1.5 kg and radius 15 cm, rod of mass .50 kg and length 60 cm. The mass swings in simple harmonic motion of maximum amplitude of /6 radians. Find...
5*) Find the angular velocity of the Earth due to its daily
rotation and express it in radians per second. Then use it, and a
model of the Earth as a solid sphere of mass M=
5.97 × 1024 kg and radius R
= 6.37 × 106 m, to estimate the angular momentum of the Earth due
to its rotation around its axis. (The result should be of the order
of 1033 kg m2/s. This is called the Earth’s “intrinsic”...
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