Question

Notify Me Bookmark

In the figure below, three thin rods are all connected at their centers. The rods each have the same length L and mass m, and they are all perpendicular to one another. Each rod lies on one of the x, y, or z-axes as shown. The entire structure formed by the rods is rotated about an axis that is parallel to the y-axis and passes through the end of the rod that lies on the x-axis. What is the moment of inertia of this structure about the axis of rotation? (Use any variable or symbol stated above as necessary. ) I =

In the figure below, three thin rods are all connected at their centers. The rods each have the same length L and mass m, and they are all perpendicular to one another. Each rod lies on one of the x, y, or z-axes as shown. The entire structure formed by the rods is rotated about an axis that is parallel to the y-axis and passes through the end of the rod that lies on the x-axis. What is the moment of inertia of this structure about the axis of rotation? (Use any variable or symbol stated above as necessary. ) I =

Image text
In the figure below, three thin rods are all connected at their centers. The rods each have the same length L and mass m , and they are all perpendicular to one another. Each rod lies on one of the x , y , or z -axes as shown. The entire structure formed by the rods is rotated about an axis that is parallel to the y -axis and passes through the end of the rod that lies on the x -axis. What is the moment of inertia of this structure about the axis of rotation? (Use any variable or symbol stated above as necessary.) (i) I =

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

The two ends of a length of chain are attached so that the chain makes a circle. If the chain is then spun very quickly, it can roll along the ground like a bicycle tire without crumpling. Consider the rolling chain shown in the figure. Assume the chain has uniform linear mass density μ and its center of mass moves to the right at a speed v0. (a) Determine the tension in the chain in terms of μ and v0. Assume the weight of an individual link is negligible compared to the tension. T = (b) If the loop rolls over a small bump, the resulting deformation of the chain causes two transverse pulses to propagate along the chain, one moving clockwise and one moving counterclockwise. What is the speed of the pulses traveling along the chain? (Use any variable or symbol stated above as necessary.) v = (c) Through what angle (in rad) does each pulse travel during the time interval over which the loop makes one revolution? (Assume the angle is measured clockwise from the ground. ) clockwise-traveling pulse rad counterclockwise-traveling pulse rad
Solution
0 0

Ball a, of mass ma, is connected to ball b, of mass mb, by a massless rod of length L. (Figure 1 )The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system about axis a is Ia, and the moment of inertia of the system about axis b is Ib. It is observed that the ratio of Ia to Ib is equal to 3: Ia Ib = 3 Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass. Figure 1 of 1 Find the ratio of the masses of the two balls. Express your answer numerically. View Available Hint(s) ma mb = Find da, the distance from ball a to the system's center of mass. Express your answer in terms of L, the length of the rod. View Available Hint(s) da =Ball a, of mass ma, is connected to ball b, of mass mb, by a massless rod of length L. (Figure 1 )The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system about axis a is Ia, and the moment of inertia of the system about axis b is Ib. It is observed that the ratio of Ia to Ib is equal to 3: Ia Ib = 3 Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass. Figure 1 of 1 Find the ratio of the masses of the two balls. Express your answer numerically. View Available Hint(s) ma mb = Find da, the distance from ball a to the system's center of mass. Express your answer in terms of L, the length of the rod. View Available Hint(s) da =Ball a, of mass ma, is connected to ball b, of mass mb, by a massless rod of length L. (Figure 1 )The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system about axis a is Ia, and the moment of inertia of the system about axis b is Ib. It is observed that the ratio of Ia to Ib is equal to 3: Ia Ib = 3 Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass. Figure 1 of 1 Find the ratio of the masses of the two balls. Express your answer numerically. View Available Hint(s) ma mb = Find da, the distance from ball a to the system's center of mass. Express your answer in terms of L, the length of the rod. View Available Hint(s) da =
Solution
0 0

Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by light rods (Figure 1) Figure 1 of 1 Part A Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane (an axis through point O in the figure). Express your answer in kilogram meters squared. I = kg⋅m2 Submit Request Answer Part B Find the moment of inertia of the system about an axis bisecting two opposite sides of the square (an axis along the line AB in the figure). Express your answer in kilogram meters squared. I = kg⋅m2 Part C Find the moment of inertia of the system about an axis that passes through the centers of the upper left and lower right spheres and through point O. Express your answer in kilogram meters squared. I = kg⋅m2Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by light rods (Figure 1) Figure 1 of 1 Part A Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane (an axis through point O in the figure). Express your answer in kilogram meters squared. I = kg⋅m2 Submit Request Answer Part B Find the moment of inertia of the system about an axis bisecting two opposite sides of the square (an axis along the line AB in the figure). Express your answer in kilogram meters squared. I = kg⋅m2 Part C Find the moment of inertia of the system about an axis that passes through the centers of the upper left and lower right spheres and through point O. Express your answer in kilogram meters squared. I = kg⋅m2Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by light rods (Figure 1) Figure 1 of 1 Part A Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane (an axis through point O in the figure). Express your answer in kilogram meters squared. I = kg⋅m2 Submit Request Answer Part B Find the moment of inertia of the system about an axis bisecting two opposite sides of the square (an axis along the line AB in the figure). Express your answer in kilogram meters squared. I = kg⋅m2 Part C Find the moment of inertia of the system about an axis that passes through the centers of the upper left and lower right spheres and through point O. Express your answer in kilogram meters squared. I = kg⋅m2
Solution
0 0