13. Rotational Inertia & Energy

An object whose moment of inertia is 4.0 kg m² is rotating with angular velocity 0.25 rad/s. It then experiences the torque shown in FIGURE EX12.25. What is the object's angular velocity at t = 3.0s?

The three masses shown in FIGURE EX12.15 are connected by massless, rigid rods. Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page.

The three 200 g masses in FIGURE EX12.11 are connected by massless, rigid rods. What is the triangle's kinetic energy if it rotates about the axis at 5.0 rev/s?

Calculate the moment of inertia of the rectangular plate in FIGURE P12.55 for rotation about a perpendicular axis through the center.

The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods. Find the moment of inertia about a diagonal axis that passes through masses B and D.

A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ = cx² , where x is measured from the center of the rod and c is a constant. Find an expression in terms of L and M for the moment of inertia of the rod for rotation about an axis through the center.

A 70.0-kg person stands on a tiny rotating platform with arms outstretched. Estimate the moment of inertia of the person using the following approximations: the body (including head and legs) is a 62.0-kg cylinder, 16 cm in radius and 1.70 m high; and each arm is a 4.0-kg thin rod, 60.0 cm long, attached to the cylinder.

A 12-cm-diameter DVD has a mass of 21 g. What is the DVD’s moment of inertia for rotation about a perpendicular axis through its center?