Angular Momentum Conservation

• Scenario: Drop a small mass on a spinning disc.
• The disc's inertia with the mass > inertia of disc alone.
• Friction between the mass and disc
• Accelerates the mass.
• Decelerates the disc.
• Result: The system's angular velocity decreases to conserve angular momentum.

🌍 Real-world Example: Think of a playground carousel. If you place a heavy object on it while it's spinning, the carousel slows down due to the added weight.

• Scenario: An ice skater spins and pulls their arms tightly to their body.
• Result: The skater's angular velocity increases.

🌍 Real-world Example: Watch ice-skating competitions! When skaters want to spin faster, they pull in their arms close to their body. When they extend them, they slow down.

• Spinning Disc & Dropped Mass
  • A disc (r = 30cm, m = 1.2kg) spins freely with an angular velocity of 5.0 rads^−1. Drop a small mass (m = 0.25kg) on it.
• Result
  • Final angular velocity = 4.2 rads⁻¹.
  • Rotational energy decreased by 0.11 J due to frictional force.
• Collapsing Star
  • If a rotating star collapses and its moment of inertia decreases to 1/1000th
• Result
  • Angular velocity = 1000 times the initial.
  • Rotational kinetic energy = 1000 times the initial.
• Merry-Go-Round & Stone
  • A child sits on a merry-go-round (radius = 2.5m) and throws a stone tangentially.
• Result
  • Angular momentum of the stone = mvr.
  • Final angular velocity = 7.1 x 10⁻³ rads⁻¹.