5.5 Rotational Energy

• Rotational kinetic energy is measured in joules (J).


  True
• What is the rotational kinetic energy of a spinning top with a moment of inertia of 0.05 kg·m² and an angular velocity of 20 rad/s?

  10 J
• What is the rotational kinetic energy of a spinning disk with a moment of inertia of 2 kg·m² and an angular velocity of 5 rad/s?

  25 J
• The total kinetic energy of an object rotating around a fixed axis is the sum of its rotational and linear kinetic energies.
• Moment of inertia depends on the object's mass and the distribution of that mass around the axis of rotation
• Moment of inertia is a measure of an object's resistance to rotational acceleration
• The formula for rotational kinetic energy is K.E. = \frac{1}{2} * I * \omega^{2}</latex>, where $I$ represents moment of inertia
• Rotational kinetic energy depends on moment of inertia and angular velocity, while linear kinetic energy depends on mass and linear velocity.

  True
• What is the rotational kinetic energy of a spinning disc with a moment of inertia of 2 kg·m² rotating at 5 rad/s?

  25 J
• The rotational kinetic energy of an object increases if its moment of inertia or angular velocity increases.


  True
• A spinning disc with a moment of inertia of 2 kg·m² rotating at 5 rad/s has a rotational kinetic energy of 25 J
• The key difference between rotational and linear kinetic energy is that rotational kinetic energy depends on moment of inertia and angular velocity, while linear kinetic energy depends on mass and linear velocity
• Moment of inertia depends on the object's mass and its mass distribution around the axis of rotation
• Match the property with its definition:

  Moment of inertia ↔️ Resistance to rotational acceleration

  Rotational kinetic energy ↔️ Energy due to rotation
• A 2 kg·m² object rotates at 5 rad/s, its rotational kinetic energy is 25 J.
• Match the physical situation with its application of rotational energy:

  Spinning Top ↔️ Maintains motion using rotational energy

  Motor ↔️ Transfers power using gears

  Rolling Wheel ↔️ Combines rotational and translational kinetic energy

  Planet ↔️ Contributes to angular momentum
• The formula for rotational kinetic energy is 1 / 2 * I * $\omega^{2}$.
• The rotational kinetic energy of an object depends on its moment of inertia and angular velocity.
• Steps to solve rotational kinetic energy problems:

  1️⃣ Identify the moment of inertia (I) and angular velocity (ω)

  2️⃣ Apply the formula $K.E. =$$\frac{1}{2} *$$I *$$\omega^{2}$

  3️⃣ Ensure units are in SI form (kg·m² and rad/s)

  4️⃣ Calculate the rotational kinetic energy
• Rotational kinetic energy depends on the object's moment of inertia
• Match the variable with its unit:

  K.E. ↔️ Joules (J)

  I ↔️ kg·m²

  ω ↔️ rad/s
• The unit for moment of inertia is kg·m²
• Rotational kinetic energy depends on mass and linear velocity.

  False
• What does moment of inertia measure?

  Resistance to rotational acceleration
• Match the variable with its description:

  K.E. ↔️ Rotational kinetic energy

  I ↔️ Moment of inertia

  ω ↔️ Angular velocity
• Rotational kinetic energy is the energy an object possesses due to its rotation.


  True
• Match the variable with its description and units:

  K.E. ↔️ Rotational kinetic energy in Joules

  I ↔️ Moment of inertia in kg·m²

  ω ↔️ Angular velocity in rad/s
• Rotational kinetic energy depends on two key factors: moment of inertia and angular velocity
• Order the steps for calculating rotational kinetic energy:

  1️⃣ Identify the moment of inertia (I)

  2️⃣ Identify the angular velocity (ω)

  3️⃣ Apply the formula: $K.E. =$$\frac{1}{2} *$$I *$$\omega^{2}$

  4️⃣ Calculate the rotational kinetic energy
• What is the formula for linear kinetic energy?

  K.E. = \frac{1}{2} * m * v^{2}</latex>
• A rolling cylinder has both rotational and linear kinetic energy.


  True
• What is the rotational kinetic energy of a cylinder with a moment of inertia of 2 kg·m² rotating at 5 rad/s?

  25 J
• Rotational energy is crucial in various physical situations, such as rotating machinery and planetary movements
• Rotational energy is significant in rotating machinery, planetary movements, and spinning objects.

  True
• Steps to identify rotational energy in a scenario:

  1️⃣ Is the object rotating around an axis?

  2️⃣ Does the object have a non-zero moment of inertia?

  3️⃣ Is the object rotating at a measurable angular velocity?
• Match the concept with its corresponding property:

  Rotational Kinetic Energy ↔️ Depends on moment of inertia and angular velocity

  Linear Kinetic Energy ↔️ Depends on mass and linear velocity
• The total kinetic energy of an object is the sum of its rotational and linear kinetic energies.


  True
• A disk with a moment of inertia of 2 kg·m² rotates at 5 rad/s, its rotational kinetic energy is 25 J.