6.4 Conservation of Angular Momentum

• What does angular momentum measure?

  Tendency to continue spinning
• What is the net external torque required for angular momentum to be conserved?

  Zero
• Why does an ice skater spin faster when they pull their arms closer to their body?

  Rotational inertia decreases
• Match the term with its definition:

  Angular Momentum ↔️ The tendency of a rotating object to continue spinning

  Rotational Inertia ↔️ The resistance to changes in rotational motion

  Angular Velocity ↔️ The rate of rotation in radians per second
• The rotational inertia of an object is represented by the symbol I
• What is the formula for rotational inertia?

  $I =$$Σmr²$
• What condition is necessary for angular momentum to be conserved?

  Net external torque = 0
• If a net external torque is present, angular momentum changes
• When a spinning top slows down due to friction, its rotational inertia decreases, and its angular velocity increases
• The units of angular momentum are kg·m²/s
• The principle of conservation of angular momentum states that the total angular momentum remains constant if the net external torque is zero.
• The conservation of angular momentum principle applies to an isolated system.
• What is the angular momentum of a spinning wheel with rotational inertia 2 kg·m² and angular velocity 3 rad/s?

  6 kg·m²/s
• The angular velocity of an object is represented by the symbol ω
• Angular velocity is the rate of rotation measured in radians
• If there is no net external torque on a system, its angular momentum remains constant.

  True
• The conservation of angular momentum applies to isolated systems.


  True
• How do divers conserve angular momentum during somersaults?

  Tuck their body into a ball
• The formula for angular momentum is L = Iω


  True
• Angular momentum changes when the net external torque is non-zero.


  True
• Steps to apply conservation of angular momentum in problem-solving

  1️⃣ Identify scenarios where angular momentum is likely conserved

  2️⃣ Define initial and final states of the system

  3️⃣ Apply the formula I₁ω₁ = I₂ω₂

  4️⃣ Plug in known values and solve

  5️⃣ Verify the answer
• The principle of conservation of angular momentum states that the initial angular momentum equals the final angular momentum if the net external torque is zero.

  True
• What is the formula for angular momentum?

  $L =$$Iω$
• Steps to apply the conservation of angular momentum principle

  1️⃣ Identify scenarios where angular momentum is likely conserved

  2️⃣ Define initial and final states

  3️⃣ Apply the formula I₁ω₁ = I₂ω₂

  4️⃣ Solve for the unknown variable

  5️⃣ Verify the answer
• Give an example of angular momentum conservation in real life.

  Ice skater pulling arms inward
• What happens to an ice skater's angular velocity when they pull their arms inward?

  Increases