(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 downward. The magnitude of the acceleration due to gravity is equal to g.
Part A
What is the moment of inertia I of this assembly about the axis through which it is pivoted?
Homework Answers
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(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 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...
(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...
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...
Need help with part C. Thank you! This is the figure above. However, it has different...
Need help with part C. Thank you!
This is the figure above. However, it has different values than
the homework question above.
PRACTICE IT Use the worked example above to help you solve this problem. A woman of mass m = 53.6 kg sits on the left end of a seesaw-a plank of length L = 4.39 m, pivoted in the middle as shown in the figure. (a) First compute the torques on the seesaw about an axis that passes...
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...
The figure shows a long, nonconducting, massless rod of length L, pivoted at its center and...
The figure shows a long, nonconducting, massless rod of length L, pivoted at its center and balanced with a block of weight W at a distance x from the left end. At the left and right ends of the rod are attached small conducting spheres with positive charges q and 2q, respectively. A distance h directly beneath each of these spheres is a fixed sphere with positive charge Q. (a) Find equation for the distance x when the rod is...
In the figure, a thin uniform rod (mass 4.6 kg, length 5.0 m) rotates freely about...
In the figure, a thin uniform rod (mass 4.6 kg, length 5.0 m) rotates freely about a horizontal axis A that is perpendicular to the rod and passes through a point at a distance d = 1.4 m from the end of the rod. The kinetic energy of the rod as it passes through the vertical position is 18 J. (a) what is the rotational inertia of the rod about axis A? (b) what is the (linear) speed of the...
L- Pivot Point 13.) A uniform, thin rod of length L and mass M is allowed to pivot about its end,...
L- Pivot Point 13.) A uniform, thin rod of length L and mass M is allowed to pivot about its end, as shown in the figure above (a) Using integral calculus, derive the rotational inertia for the rod around its end to show that it is ML2/3 The rod is fixed at one end and allowed to fall from the horizontal position A through the vertical position B. (b) Derive an expression for the velocity of the free end of...
The figure below shows a thin rod, of length L and negligible mass, that can pivot about one end to rotate in a vertical circle.
The figure below shows a thin rod, of length L and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m is attached to the other end. The rod is pulled aside through an angle and released. (a) What is the speed of the ball at the lowest point if L = 1.30 m, θ = 32.0°, and m = 500 kg? (b) Does the speed increase, decrease, or remain the same...
A slender, uniform metal rod of mass M and length l is pivoted without friction about an axis through its midpoint and p...
A slender, uniform metal rod of mass M and length l is pivoted
without friction about an axis through its midpoint and
perpendicular to the rod. A horizontal spring, assumed massless and
with force constant k, is attached to the lower end of the rod,
with the other end of the spring attached to a rigid support.
(Figure 1)
2. Find the torque τ due to the spring. Assume that θ is small
enough that the spring remains effectively horizontal...
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...
Need help with part C. Thank you!
This is the figure above. However, it has different values than
the homework question above.
PRACTICE IT Use the worked example above to help you solve this problem. A woman of mass m = 53.6 kg sits on the left end of a seesaw-a plank of length L = 4.39 m, pivoted in the middle as shown in the figure. (a) First compute the torques on the seesaw about an axis that passes...
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...
The figure shows a long, nonconducting, massless rod of length L, pivoted at its center and balanced with a block of weight W at a distance x from the left end. At the left and right ends of the rod are attached small conducting spheres with positive charges q and 2q, respectively. A distance h directly beneath each of these spheres is a fixed sphere with positive charge Q. (a) Find equation for the distance x when the rod is...
In the figure, a thin uniform rod (mass 4.6 kg, length 5.0 m) rotates freely about a horizontal axis A that is perpendicular to the rod and passes through a point at a distance d = 1.4 m from the end of the rod. The kinetic energy of the rod as it passes through the vertical position is 18 J. (a) what is the rotational inertia of the rod about axis A? (b) what is the (linear) speed of the...
L- Pivot Point 13.) A uniform, thin rod of length L and mass M is allowed to pivot about its end, as shown in the figure above (a) Using integral calculus, derive the rotational inertia for the rod around its end to show that it is ML2/3 The rod is fixed at one end and allowed to fall from the horizontal position A through the vertical position B. (b) Derive an expression for the velocity of the free end of...
A slender, uniform metal rod of mass M and length l is pivoted
without friction about an axis through its midpoint and
perpendicular to the rod. A horizontal spring, assumed massless and
with force constant k, is attached to the lower end of the rod,
with the other end of the spring attached to a rigid support.
(Figure 1)
2. Find the torque τ due to the spring. Assume that θ is small
enough that the spring remains effectively horizontal...
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