Physics
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A thin light cord is wound around a pulley of diameter 20 cm and mass 1 kg. The pulley is considered to be a thin hoop. Determine the moment of inertia of the pulley around an axis perpendicular to the pulley's plane and passing through the cord.
A metal piece of mass M is extended to form a planar rectangular sheet. If the length of the sheet L is twice the width, find the moment of inertia about an axis perpendicular to the sheet and passing through one of the four corners.
You make a corner weld between two thin uniform rods of mass 1 kg and length 3 m each. In this situation, the two rods are perpendicular to each other. Determine the moment of inertia about an axis perpendicular to the plane of this system and passing through the welding point.
Two tiny iron spheres are welded to a homogenous metallic antenna. The spheres have a mass of 25 g each, whereas the antenna is 1 m long and has a mass of 250 g. Assume that the size of the spheres is small compared to the length of the antenna. Calculate the moment of inertia of this system about a fixed axis parallel to the antenna. The distance between the axis and the antenna is 15 cm.
A cylinder of mass M, radius R, and length L is tightly fitted with an axle that acts like a rotational axis at a distance (3/5)R from the center of the cylinder. The axle has a radius r. A thread wound on the axle is pulled with a tension T. Assuming the axle to have an insignificant moment of inertia, derive an expression for the cylinder's angular acceleration.
What will be the moment of inertia for a gate that is 2.6 m tall and 1.1 m wide and weighs 20 kg, about its pivot at one edge, and assuming that the gate's thickness is negligible?