Assessment: Rotational Dynamics

What kind of quantity does the scalar (dot) product of two vectors produce?

Why does moment of inertia depend on r² rather than just r?

An object has zero net force acting on it. Is it necessarily in complete equilibrium?

A 40 N force acts at 90° to a 0.5 m lever arm. Find the torque.

A rotor with moment of inertia 3.5 kg·m² spins at 6 rad/s. Find its angular momentum.

A net torque of 18 N·m produces an angular acceleration of 3 rad/s² in a rotating disc. Find the moment of inertia.

A diver spinning at 4 rad/s with I₁ = 8 kg·m² (tucked) straightens out to I₂ = 16 kg·m². Find the new angular velocity (no external torque).

Why does a collapsing star spin dramatically faster as it shrinks into a neutron star?

Why are door handles placed far from the hinge rather than close to it?

A force is applied exactly along the direction of a lever arm (parallel to it, θ = 0°). What torque results, and why?