A figure skater spinning with arms outstretched pulls her arms in tightly. Assuming no external torque acts, what happens to her angular speed?
AIt decreases, because she has less rotational inertia.
BIt stays the same, because no external torque acts.
CIt increases, because angular momentum is conserved and her moment of inertia decreases.
DIt increases, because pulling her arms in applies an internal torque.
With no external torque, angular momentum L = Iω is conserved. Pulling arms inward reduces moment of inertia I. Since L = Iω must stay constant, ω must increase. This is why skaters spin faster when they pull in — not because of any external force, but because L is fixed and I shrinks.
Question 2 True / False
A hockey puck sliding in a straight line across frictionless ice has zero angular momentum with respect to any reference point you choose.
TTrue
FFalse
Answer: False
Angular momentum L = r × p depends on the reference point chosen. For a puck with momentum p moving in a straight line, if you choose a reference point that is NOT on the line of motion, then r has a nonzero perpendicular component, giving L = mvr⊥ ≠ 0. Only if the reference point lies exactly on the line of motion is L zero. This illustrates that angular momentum is not exclusive to spinning or curved-path motion.
Question 3 Short Answer
In what sense is angular momentum the rotational analog of linear momentum? Identify one equation that makes this analogy precise.
Think about your answer, then reveal below.
Model answer: Just as F = dp/dt relates net force to the rate of change of linear momentum, the equation Στ = dL/dt relates net torque to the rate of change of angular momentum. L = Iω parallels p = mv, with moment of inertia I playing the role of mass and angular velocity ω playing the role of linear velocity.
The analogy runs deep: mass ↔ moment of inertia, velocity ↔ angular velocity, force ↔ torque, linear momentum ↔ angular momentum. Every theorem about linear momentum has a rotational counterpart. Recognizing this parallel dramatically reduces what you need to memorize — you can derive rotational results from linear ones by substitution.