6.1 Rotational Kinetic Energy

• Rotational kinetic energy is calculated using the formula: KE_{rot} = \frac{1}{2}I\omega^2
• What does the variable \(m_i\) represent in the formula for moment of inertia?

  Mass of each particle
• The formula for translational kinetic energy is: KE_{trans} = \frac{1}{2}mv^{2}
• The formula for translational kinetic energy is $KE_{trans} =$$\frac{1}{2}mv^{2}$.


  True
• Rotational kinetic energy depends on mass and linear velocity.

  False
• The moment of inertia measures an object's resistance to changes in rotational motion.

  True
• What is an example of translational kinetic energy?

  Moving car
• In the formula for rotational kinetic energy, the variable 'I' represents the moment of inertia.
• Give an example of an object with rotational kinetic energy.

  Spinning wheel
• Steps to apply the rotational kinetic energy formula in real-world scenarios:

  1️⃣ Identify the rotating object

  2️⃣ Determine its moment of inertia

  3️⃣ Measure or calculate the angular velocity

  4️⃣ Substitute the values into the formula

  5️⃣ Solve for KE_{rot}
• What is the rotational kinetic energy of a wind turbine with a moment of inertia of 5000 kg·m² and an angular velocity of 0.5 rad/s?

  625 J
• What is rotational kinetic energy?

  Energy due to rotation
• The formula for moment of inertia is: I = \sum m_i r_i^2
• What type of motion is associated with rotational kinetic energy?

  Rotational motion
• The formula for rotational kinetic energy is: KE_{rot} = \frac{1}{2}I\omega^{2}
• What is the unit for angular velocity?

  rad/s
• A spinning wheel with I = 2 kg·m² and ω = 5 rad/s has what rotational kinetic energy?

  25 J
• Rotational kinetic energy is associated with rotational motion.
• What is the formula for rotational kinetic energy?

  $KE_{rot} =$$\frac{1}{2}I\omega^{2}$
• Match the feature with the correct type of kinetic energy:

  Rotation ↔️ Rotational Kinetic Energy

  Linear Motion ↔️ Translational Kinetic Energy
• What is the rotational kinetic energy of a spinning wheel with a moment of inertia of 2 kg·m² and an angular velocity of 5 rad/s?

  25 J
• To calculate rotational kinetic energy, you must first determine the object's mass.

  False
• What does the variable \(I\) represent in the formula for rotational kinetic energy?

  Moment of inertia
• Greater mass always results in a smaller moment of inertia.

  False
• What are the variables in the formula for translational kinetic energy?

  Mass and linear velocity
• What is an example of rotational kinetic energy?

  Spinning wheel
• Rotational kinetic energy depends on the moment of inertia and angular velocity.
• Key factors influencing the moment of inertia include mass and mass distribution.
• The formula for rotational kinetic energy is $KE_{rot} =$$\frac{1}{2}I\omega^{2}$.


  True
• What is the unit of angular velocity in the rotational kinetic energy formula?

  rad/s
• The rotational kinetic energy of an object increases as its angular velocity increases.


  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 30 rad/s?

  22.5 J
• Moment of inertia depends on an object's mass and the distribution of that mass relative to the axis of rotation.


  True
• Match the variables in the rotational kinetic energy formula with their descriptions and units.

  KE_{rot} ↔️ Rotational kinetic energy (J)

  I ↔️ Moment of inertia (kg m²)

  \(\omega\) ↔️ Angular velocity (rad/s)
• Rotational and translational kinetic energy are both measured in Joules.


  True
• What is the unit for moment of inertia?

  kg·m²
• Why does a long, thin rod have a larger moment of inertia than a short, thick rod of the same mass?

  Mass is further from axis
• The angular velocity in the rotational kinetic energy formula is measured in rad/s.
• Rotational kinetic energy is based on linear velocity.

  False
• The moment of inertia in the rotational kinetic energy formula is measured in kg·m².