Problem Statement
A ball of mass m is attached to a string and moves in a horizontal circle of radius r₁ with speed v₁ on a frictionless table. The string is shortened to r₂. Find the new speed v₂.
Given
m, r₁, v₁, r₂. Frictionless, string tension is central force (no torque about center).
Concepts & Formulas
Conservation of angular momentum: m·v₁·r₁ = m·v₂·r₂ → v₂ = v₁r₁/r₂.
Step-by-Step Solution
Step 1: No torque about center (tension is central). L = const.
Step 2: L = m·v·r → m·v₁·r₁ = m·v₂·r₂.
Step 3: v₂ = v₁r₁/r₂.
Worked Calculation
v₂ = v₁r₁/r₂.
Boxed Answer
v₂ = v₁r₁/r₂
Physical Interpretation
Like a spinning skater pulling in arms, reducing the radius increases the speed — angular momentum is redistributed from radius to velocity.
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