6.2 Conservation Laws in Rotational Motion

• What is rotational kinetic energy the result of?

  Rotational motion
• The formula for rotational kinetic energy is KE_rot = 1/2 * I * ω^2
• What does the moment of inertia (I) represent in rotational kinetic energy?

  Resistance to rotation
• Angular velocity (ω) indicates how fast an object is rotating.
• What is the rotational kinetic energy of a spinning top with a moment of inertia of 0.02 kg·m^2 and an angular velocity of 10 rad/s?

  1 J
• Match the variable with its definition:

  Rotational Kinetic Energy ↔️ Energy due to rotation

  Moment of Inertia ↔️ Resistance to rotational motion

  Angular Velocity ↔️ Rate of rotation
• What is the Law of Conservation of Angular Momentum in words?

  Angular momentum remains constant
• The Law of Conservation of Angular Momentum is mathematically expressed as L = Iω = constant
• What is the unit for angular momentum (L)?

  kg·m²/s
• A figure skater increases their angular velocity by reducing their moment of inertia.
• Match the concept with its definition:

  Angular Momentum ↔️ Measure of an object's rotation

  Moment of Inertia ↔️ Resistance to rotational motion

  Angular Velocity ↔️ Rate of rotation
• The formula for rotational kinetic energy is KE_rot = 1/2 * I * ω^2
• What does the variable I represent in the formula for rotational kinetic energy?

  Moment of inertia
• Angular velocity is measured in rad/s.
• What is the rotational kinetic energy of a toy top with a moment of inertia of 0.02 kg·m^2 and an angular velocity of 10 rad/s?

  1 J
• Match the variable with its definition and units:

  Rotational Kinetic Energy ↔️ Energy due to rotation, J

  Moment of Inertia ↔️ Resistance to rotational motion, kg·m^2

  Angular Velocity ↔️ Rate of rotation, rad/s
• What is the mathematical expression for the Law of Conservation of Angular Momentum?

  L = Iω = constant
• In the Law of Conservation of Angular Momentum, L represents angular momentum
• What does I stand for in the Law of Conservation of Angular Momentum?

  Moment of inertia
• A figure skater reduces their moment of inertia by pulling their arms in.
• What is the unit for angular momentum (L)?

  kg·m²/s
• Match the concept with its symbol and unit:

  Angular Momentum ↔️ L, kg·m²/s

  Moment of Inertia ↔️ I, kg·m²

  Angular Velocity ↔️ ω, rad/s
• What happens to the angular velocity of a figure skater when they pull their arms in, according to the Law of Conservation of Angular Momentum?

  Increases
• The Conservation of Angular Momentum states that L_initial = L_ final
• Conservation of energy includes both translational and rotational kinetic energy.
• What is the final velocity of a bowling ball rolling without slipping down an incline from height h, using conservation of energy?

  $\sqrt{\frac{10}{7}gh}$
• Steps to solve rotational motion problems using conservation laws:

  1️⃣ Identify the relevant conservation principle

  2️⃣ Define initial and final states

  3️⃣ Apply the conservation equations

  4️⃣ Solve for the unknowns
• What does the moment of inertia measure?

  Resistance to rotation
• Kinetic energy can be translational (KE = 1/2mv²) or rotational
• KE_initial + PE_initial = KE_final + PE_final
• A roller coaster gains kinetic energy and loses potential energy as it ascends a hill.

  False
• Steps to solve rotational motion problems using conservation laws:

  1️⃣ Identify the relevant conservation principle

  2️⃣ Define initial and final states

  3️⃣ Apply the conservation equations

  4️⃣ Solve for the unknowns
• What is the final velocity of a bowling ball rolling without slipping down an incline from height h, using conservation of energy?

  $\sqrt{\frac{10}{7}gh}$
• The moment of inertia is a measure of an object's resistance to changes in its rotational motion
• What is the formula for the moment of inertia?

  $I =$$\sum mr^{2}$
• Match the variable with its definition and unit:

  Moment of Inertia ↔️ Resistance to rotational motion, kg·m²

  Mass ↔️ Mass of each particle, kg

  Distance from Axis ↔️ Distance of each particle from the axis of rotation, m
• What is the formula for rotational kinetic energy?

  $KE_{rot} =$$\frac{1}{2}I\omega^{2}$
• In the rotational kinetic energy formula, ω represents the angular velocity
• The Law of Conservation of Angular Momentum states that the total angular momentum of a closed system remains constant if no external torques act upon it.
• What is the mathematical expression for the Law of Conservation of Angular Momentum?

  $L =$$I\omega =$$constant$