The moment of inertia of a thin wire bent in the shape of a semicircle about the diameter is I = 3/8 MR^2.

The moment of inertia of a rectangular plate about an axis through its center and parallel to side a is I = 1/3 Mb^2.

The moment of inertia of a uniform thin circular plate about an axis through its center and perpendicular to its plane is I = 1/2 MR^2.

The moment of inertia of a square plate about an axis through its center and parallel to one side is I = 1/12 Ma².

Angular momentum L is given by L = Iω, where ω is the angular velocity.

The relationship is given by v = ωr, where r is the radius of the rotation.

The relationship is given by τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration.

Torque = Force × Distance = 8 N × 0.75 m = 6 Nm.

Torque = Force × Distance = 60 N × 0.75 m = 45 Nm.

Torque = Force × Distance = 60 N × 0.75 m = 45 Nm.

Torque (τ) = Force (F) × Distance (r) = 10 N × 2 m = 20 Nm.

Torque = Force × Distance × sin(θ) = 15 N × 0.5 m × sin(90°) = 15 Nm.

Torque = Force × Distance × sin(90°) = 25 N × 0.5 m × 1 = 12.5 Nm.

The unit of angular momentum is kg·m^2/s.

The unit of torque in the SI system is Newton-meter (Nm).

The acceleration of the center of mass of a wheel rolling down an incline is g sin(θ).

The distance traveled by the center of mass d is equal to the product of the radius R and the angle rotated θ in radians, i.e., d = Rθ.

The mass of the object does not affect the torque; torque depends on the force, distance from the pivot, and angle of application.

The mass of the object does not affect the torque; torque depends on force, distance, and angle.

The solid sphere has the smallest moment of inertia compared to the other shapes for the same mass and radius.

In a closed system, angular momentum is conserved, while linear momentum and kinetic energy may not be.

In a closed system with no external torques, angular momentum is conserved.

In a closed system with no external torques, angular momentum is conserved.

In an isolated system with no external torques, angular momentum is conserved.

In the absence of external torques, angular momentum is conserved.

The hollow sphere has the largest moment of inertia compared to the other shapes for the same mass and radius.

Torque depends on the angle of application, as it is calculated using τ = F × d × sin(θ).

The moment of inertia depends on the mass distribution relative to the axis of rotation.

The parallel axis theorem is used to find the moment of inertia about an axis parallel to one through the center of mass.