(Figure 1) A thin rod of mass mr and length 2L is allowed to pivot freely about its center, as shown in the diagram.
Pivoted Rod with Unequal Masses
(Figure 1) A thin rod of mass mr and length 2L is allowed to pivot freely about its center, as shown in the diagram. A small sphere of mass m1 is attached to the left end of the rod, and a small sphere of mass m2 is attached to the right end. The spheres are small enough that they can be considered point particles. The gravitational force acts downward, with the magnitude of the gravitational acceleration equal to g.
Part A
What is the moment of inertia I of this assembly about the axis through which it is pivoted?
Part B
Suppose the rod is held at rest horizontally and then released. (Throughout the remainder of this problem, your answer may include the symbol I, the moment of inertia of the assembly, whether or not you have answered the first part correctly.)
What is the angular acceleration a of the rod immediately after it is released?
Homework Answers
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(Figure 1) A thin rod of mass mr and length 2L is allowed to pivot freely about its center, as shown in the diagram.
(Figure 1)The figure shows a simple model of a seesaw These consist of a plank/rod of mass mr and length 2x allowed to pivot freely about its center (or central axis), as shown in the diagram.
(Figure 1)The figure shows a simple model of a seesaw These consist of a plank/rod of mass mr and length 2x allowed to pivot freely about its center (or central axis), as shown in the diagram. A small sphere of mass m1 is attached to the left end of the rod, and a small sphere of mass m2 is attached to the right end. The spheres are small enough that they can be considered point particles. The gravitational force acts...
(Figure 1) The figure shows a simple model of a seesaw. These consist of a plank/rod of mass mr and length 2x allowed t...
(Figure 1) The figure shows a simple model of a seesaw. These consist of a plank/rod of mass mr and length 2x allowed to pivot freely about its center (or central axis), as shown in the diagram. A small sphere of mass m1 is attached to the left end of the rod, and a small sphere of mass m2 is attached to the right end. The spheres are small enough that they can be considered point particles. The gravitational force...
A uniform rod of mass M = 5.14kg and length L = 1.01m can pivot freely...
A uniform rod of mass M = 5.14kg and length L = 1.01m can pivot
freely (i.e., we ignore friction) about a hinge attached to a wall,
as seen in the figure below.
The rod is held horizontally
and then released. At the moment of release, determine the angular
acceleration of the rod. Use units of rad/s^2.
Determine the linear acceleration of the tip of the rod. Assume
that the force of gravity acts at the center of mass of...
A uniform rod of mass M = 5.02kg and length L = 1.08m can pivot freely...
A uniform rod of mass M = 5.02kg and length L = 1.08m can pivot
freely (i.e., we ignore friction) about a hinge attached to a wall,
as seen in the figure below.
The rod is held horizontally and then released. At the moment of
release, determine the angular acceleration of the rod. Use units
of rad/s^2.
Mg L L2
1. A uniform rod of mass M = 5.01kg and length L = 1.18m can pivot...
1. A uniform rod of mass M = 5.01kg and length L = 1.18m can
pivot freely (i.e., we ignore friction) about a hinge attached to a
wall, as seen in the figure below.
2. Determine the linear acceleration of the tip of the rod.
Assume that the force of gravity acts at the center of mass of the
rod, as shown.
Please show work for both questions
radusn2. The rod is held horizontally and then released. At the moment...
Example 10.8 Rotating Rod A uniform rod of length L 1.6 m and mass 2.8 k...
Example 10.8 Rotating Rod A uniform rod of length L 1.6 m and mass 2.8 k is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in the figure. The rod is released from rest in the horizontal position. What are the initial angular acceleration of the rod and the initial translational acceleration of its right end Pivot SOLVE IT Mg A rod is free to rotate around...
AXis Two spheres of mass m are attached to a light rod of length 2L. The...
AXis Two spheres of mass m are attached to a light rod of length 2L. The rod is fixed at its center to a freely-rotating axis. The rod is horizontal when a small bird of mass 5m carefully lands on the right sphere. Express a answers in terms of m, L, and g (a) What is the net torque on the system the instant the bird lands (while the rod is still horizontal)? (b) Determine the angular acceleration of the...
A uniform rod of mass m-6 kg has length L = 60 cm . Instead of...
A uniform rod of mass m-6 kg has length L = 60 cm . Instead of pivoting it at its end, we pivoted it at L/3 from the end as shown in the figure, we now set the rod into small angle oscillations. What is the period of the oscillation given that the moment of inertia about the pivot point is ml2/9? L/3 Pivot L С.М. 2L/3
A uniform rod of mass m- 9 kg has length L-70 cm. Instead of pivoting it...
A uniform rod of mass m- 9 kg has length L-70 cm. Instead of pivoting it at its end, we pivoted it at L/3 from the end as shown in the figure. We now set the rod into small angle oscillations. What is the period of the oscillation given that the moment of inertia about the pivot point is mL2/9? L/3 Pivot L с.м. 2L/3
An object is formed by attaching a uniform, thin rod with a mass of mr =...
An object is formed by attaching a uniform, thin rod with a mass of mr = 7.31 kg and length L = 5.68 m to a uniform sphere with mass ms = 36.55 kg and radius R = 1.42 m. Note ms = 5mr and L = 4R. *What is the moment of inertia of the object about an axis at the left end of the rod? *If the object is fixed at the left end of the rod, what...
A uniform rod of mass M = 5.14kg and length L = 1.01m can pivot
freely (i.e., we ignore friction) about a hinge attached to a wall,
as seen in the figure below.
The rod is held horizontally
and then released. At the moment of release, determine the angular
acceleration of the rod. Use units of rad/s^2.
Determine the linear acceleration of the tip of the rod. Assume
that the force of gravity acts at the center of mass of...
A uniform rod of mass M = 5.02kg and length L = 1.08m can pivot
freely (i.e., we ignore friction) about a hinge attached to a wall,
as seen in the figure below.
The rod is held horizontally and then released. At the moment of
release, determine the angular acceleration of the rod. Use units
of rad/s^2.
Mg L L2
1. A uniform rod of mass M = 5.01kg and length L = 1.18m can
pivot freely (i.e., we ignore friction) about a hinge attached to a
wall, as seen in the figure below.
2. Determine the linear acceleration of the tip of the rod.
Assume that the force of gravity acts at the center of mass of the
rod, as shown.
Please show work for both questions
radusn2. The rod is held horizontally and then released. At the moment...
Example 10.8 Rotating Rod A uniform rod of length L 1.6 m and mass 2.8 k is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in the figure. The rod is released from rest in the horizontal position. What are the initial angular acceleration of the rod and the initial translational acceleration of its right end Pivot SOLVE IT Mg A rod is free to rotate around...
AXis Two spheres of mass m are attached to a light rod of length 2L. The rod is fixed at its center to a freely-rotating axis. The rod is horizontal when a small bird of mass 5m carefully lands on the right sphere. Express a answers in terms of m, L, and g (a) What is the net torque on the system the instant the bird lands (while the rod is still horizontal)? (b) Determine the angular acceleration of the...
A uniform rod of mass m-6 kg has length L = 60 cm . Instead of pivoting it at its end, we pivoted it at L/3 from the end as shown in the figure, we now set the rod into small angle oscillations. What is the period of the oscillation given that the moment of inertia about the pivot point is ml2/9? L/3 Pivot L С.М. 2L/3
A uniform rod of mass m- 9 kg has length L-70 cm. Instead of pivoting it at its end, we pivoted it at L/3 from the end as shown in the figure. We now set the rod into small angle oscillations. What is the period of the oscillation given that the moment of inertia about the pivot point is mL2/9? L/3 Pivot L с.м. 2L/3
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