A thin, rectangular sheet of metal has mass M and sides of length a and b....

A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b. Express your answer in terms of some or all of the variables M, a, and b

Find the moment of inertia of the plate for an axis that lies in the plane of the plate, passes through the center of the plate, and is perpendicular to the axis in part A.

Express your answer in terms of some or all of the variables M, a, and b.

Solutions

Expert Solution

Please have a look at the solution below:

Here I have marked the length of AD as D

but in this problem D = a

Please replace D by a in the above solution.

Thus:

similarly:

Thus by perpendicular axis theorem:

genius_generous answered 2 days ago

Next > < Previous

Related Solutions

A stepladder consists of two sides of equal mass and a length of 3.7 m, and...

A stepladder consists of two sides of equal mass and a length of 3.7 m, and the two sides are connected by a rope fixed 1.2 m from the bottom of the ladder. When opened, the angle between the two sides of the ladder is 61°. The ladder stands on a frictionless horizontal floor. Determine the tension in the rope T and the reaction force at the top hinge if the total mass of the ladder is 17 kg. (Hint:...

A thin copper rod has a mass per unit length of 0.1 kg/m. What is the...

A thin copper rod has a mass per unit length of 0.1 kg/m. What is the minimum current in the rod that would allow it to levitate above the ground in a magnetic field of magnitude 0.5 T? (g = 10.0 m/s2) 2.9 A 2.5 A 2.2 A 2.0 A 1.8 A

A thin, uniform bar of length L and mass M is suspended horizontally at rest. It...

A thin, uniform bar of length L and mass M is suspended horizontally at rest. It is suddenly released and, at the same instant, it is struck a sharp blow vertically upwards at one end – the duration of the impulse is negligibly short. (a) Explain the meaning of the equation Fnet = Macom (com stands for center of mass). If we call z the vertical direction, write an equation for zCOM(t), draw a sketch of zCOM(t) vs t, and...

A rectangular block of copper has sides of length 12 cm, 26 cm, and 37 cm....

A rectangular block of copper has sides of length 12 cm, 26 cm, and 37 cm. If the block is connected to a 5.4 V source across two of its opposite faces, find the following. (a) What is the maximum current the block can carry? (b) What is the minimum current the block can carry?

a. Squares with sides of length x are cut out of each corner of a rectangular...

a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 5 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. b. Suppose that in part (a) the original piece of cardboard is a square with sides of length s. Find the volume of the largest box that...

A long conducting pipe has a rectangular cross section with sides of lengths a and b....

A long conducting pipe has a rectangular cross section with sides of lengths a and b. One face of the pipe is maintained at a constant potential V = V0 while the other 3 faces are grounded (V = 0). Using separation of variables, find the potential for points inside the pipe V (x,y).

A rectangular piece of metal is 30in longer than it is wide. Squares with sides 6in...

A rectangular piece of metal is 30in longer than it is wide. Squares with sides 6in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2706incubed3, what were the original dimensions of the piece of metal? what is the original width? what is the original length?

A uniform thin rod of length 0.4 m and mass 0.5 kg can rotate in a...

A uniform thin rod of length 0.4 m and mass 0.5 kg can rotate in a horizontal plane about a vertical axis on the left end of the rod. The rod is at rest when a 10.0-g bullet traveling in the horizontal plane of the rod is fired into the right end of the rod at an angle 90o with the rod. The bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after...

Attached to each end of a thin steel rod of length 1.10 m and mass 6.60...

Attached to each end of a thin steel rod of length 1.10 m and mass 6.60 kg is a small ball of mass 1.07 kg. The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint. At a certain instant, it is rotating at 39.0 rev/s. Because of friction, it slows to a stop in 32.0 s. Assuming a constant retarding torque due to friction, find the following. A) Angular Acceleration rad/sec^2 B) Retarding...

A thin rod (mass 8.28 kg, length 8.04 m) is sitting on a horizontal, frictionless table....

A thin rod (mass 8.28 kg, length 8.04 m) is sitting on a horizontal, frictionless table. There is a 0.626 kg frog sitting on the very end of the rod; you can treat the frog as a point particle. Suddenly the frog jumps off at speed 4.75 m/s, moving horizontally and perpendicular to the rod. Find ω, the angular speed of the rod after the frog jumps off, in rad/s.

Subjects