6.1 Rotational Kinetic Energy

• The formula for rotational kinetic energy is $K_\text{rot} =$$\frac{1}{2}I\omega^{2}$


  True
• Linear kinetic energy depends on mass and linear velocity, while rotational kinetic energy depends on moment of inertia and angular velocity.


  True
• Ordering the steps to differentiate between linear and rotational kinetic energy:

  1️⃣ Identify the type of motion (translational or rotational)

  2️⃣ Determine the relevant formula

  3️⃣ Note the dependencies: mass and velocity for linear, inertia and angular velocity for rotational

  4️⃣ Apply the appropriate formula to calculate the energy
• The formula for moment of inertia varies depending on the object's shape
• What is the formula for rotational kinetic energy?

  $K_\text{rot} =$$\frac{1}{2}I\omega^{2}$
• Linear kinetic energy is associated with translational movement
• What is moment of inertia a measure of?

  Resistance to rotational acceleration
• What is the moment of inertia formula for a point mass?

  $I =$$mr^{2}$
• What is the moment of inertia formula for a solid sphere?

  $I =$$\frac{2}{5}mr^{2}$
• In the moment of inertia formulas, 'r' represents the distance from the axis of rotation
• What is rotational kinetic energy defined as?

  Energy due to rotational motion
• What does 'I' represent in the rotational kinetic energy formula?

  Moment of inertia
• What does 'ω' represent in the rotational kinetic energy formula?

  Angular velocity
• What does rotational kinetic energy depend on?

  Moment of inertia, angular velocity
• Rotational kinetic energy depends on moment of inertia and angular velocity, while linear kinetic energy depends on mass and linear velocity.


  True
• What does linear kinetic energy depend on?

  Mass, linear velocity
• What is the moment of inertia formula for a point mass?

  $I =$$mr^{2}$
• The moment of inertia depends on the object's mass and the distance from the axis of rotation.


  True
• Rotational kinetic energy is measured in joules
• Angular velocity is measured in radians per second.


  True
• A solid sphere with a moment of inertia of 0.2 kg·m² rotates at 5 rad/s. Its rotational kinetic energy is 2.5 J
• What is the moment of inertia a measure of?

  Resistance to rotational changes
• What is rotational kinetic energy due to?

  Spinning around an axis
• The formula for linear kinetic energy is K_\text{lin} = \frac{1}{2}mv^{2}
• What two properties does linear kinetic energy depend on?

  Mass and linear velocity
• A higher moment of inertia makes it easier to change an object's rotational speed.

  False
• Match the object shape with its moment of inertia formula:

  Point mass ↔️ $I =$$mr^{2}$

  Solid cylinder ↔️ $I =$$\frac{1}{2}mr^{2}$

  Solid sphere ↔️ $I =$$\frac{2}{5}mr^{2}$
• What does 'm' represent in the moment of inertia formulas?

  Mass of the object
• What does 'r' represent in the moment of inertia formulas?

  Distance from rotation axis
• What is the unit of moment of inertia?

  $kg \cdot m^{2}$
• In the formula for rotational kinetic energy, $\omega$ represents the angular velocity
• Rotational kinetic energy can be expressed in terms of angular momentum and moment of inertia.


  True
• What is the rotational kinetic energy of a solid cylinder with $I =$$0.25 kg \cdot m^{2}$ and $\omega =$$6 rad / s$?


  $4.5 J$
• Rotational kinetic energy is the kinetic energy of an object due to its rotational
• Rotational kinetic energy depends on the moment of inertia and the angular velocity
• Linear kinetic energy reflects the energy needed to move an object in a straight line
• The moment of inertia measures an object's resistance to rotational acceleration.

  True
• What is the formula for linear kinetic energy?

  $K_\text{lin} =$$\frac{1}{2}mv^{2}$
• Linear kinetic energy depends on mass and linear velocity.


  True
• Rotational kinetic energy is associated with rotational movement