Productivity of a Student

When the coefficient of friction is less, the student is less productive because their stool (which is what students sit on at lab benches in physics class) is more spinny and they're having too much fun. There is a productivity asymptote, since even a non-distracted student cannot be infinitely productive.

When more mass is near the axis of rotation (arms on hips), the angular speed is greater. When more mass is farther from the axis of rotation (arms out), the angular speed is less. This difference occurs because angular momentum (L=Iw=MR^2*w) is conserved; if you make MR^2 smaller with more mass at a smaller radius, that means that angular speed w must increase to keep L the same.

Angular speed w is related to linear speed v because w=v/R. Rotational inertia I is MR^2 (sometimes times a constant). Torque = Ia, where a is alpha, the angular acceleration. Friction force = mu*Normal force when a block is sliding across a surface with friction.