5.3 Rotational Dynamics

• What is rotational dynamics the study of?

  Forces and torques causing rotation
• What is angular acceleration caused by?

  Torque
• What does Newton's Second Law for Rotation state?

  Net torque equals inertia times angular acceleration
• Match the variable with its unit:

  Torque ↔️ Newton-meters (Nm)

  Moment of Inertia ↔️ Kilogram-meter squared (kg·m²)

  Angular Acceleration ↔️ Radians per second squared (rad/s²)
• Rotational dynamics involves understanding how torque influences moment of inertia to produce angular acceleration.
• What is the unit for torque?

  Nm
• Angular acceleration is measured in rad/s².
• Moment of inertia depends on both the mass and the distribution of mass around the axis of rotation.

  True
• The distance of each small element from the axis of rotation is denoted by r_i.
• The formula for moment of inertia (\(I\)) is \(I = \sum m_i r_i^2\).
• The larger the moment of inertia, the more torque is required to achieve a given angular acceleration.
• What is angular velocity measured in?

  rad/s
• Match the concept with its definition and units:

  Angular Velocity ↔️ Rate of change of angular position (rad/s)

  Angular Acceleration ↔️ Rate of change of angular velocity (rad/s²)
• What is rotational dynamics the study of?

  Forces and torques causing rotation
• Moment of inertia measures an object's resistance to changes in rotational motion.
• When torque is applied to an object, it experiences angular acceleration.

  True
• The formula for Newton's Second Law for Rotation is \tau = I \alpha.
• To what linear motion law is Newton's Second Law for Rotation analogous?

  F = ma
• A torque of 2 Nm applied to a top with a moment of inertia of 0.5 kg·m² results in an angular acceleration of 4 rad/s².


  True
• What is the unit for moment of inertia?

  kg·m²
• What is moment of inertia a measure of?

  Resistance to rotational motion
• What does \(m_i\) represent in the moment of inertia formula?

  Mass of each small element
• What is moment of inertia a measure of?

  Resistance to rotational motion
• The term \(m_i\) in the moment of inertia formula represents the mass of each small element of the object.


  True
• Objects with more mass distributed farther from the axis of rotation are harder to rotate.

  True
• Angular acceleration is the rate of change of angular velocity over time.
• If a spinning top accelerates at 2 rad/s², its angular velocity increases by 2 rad/s every second.


  True
• Torque is measured in Newton-meters.
• What is Newton's Second Law for Rotation in formula form?

  \(\tau = I \alpha\)
• If a wheel with a moment of inertia of 2 kg·m² experiences a torque of 10 Nm, its angular acceleration is 5 rad/s².


  True
• What is the definition of torque?

  Force causing rotation
• Angular acceleration is measured in rad/s².


  True
• Moment of inertia depends on the mass distribution around the axis of rotation
• What is the moment of inertia of a solid cylinder with a mass of 10 kg and a radius of 0.2 m?

  0.2 kg·m²
• A spinning top accelerates from 5 rad/s to 15 rad/s over 5 seconds. What is its angular acceleration?

  2 rad/s²
• Match the concept in linear motion with its equivalent in rotational motion:

  Force ↔️ Torque

  Mass ↔️ Moment of Inertia

  Acceleration ↔️ Angular Acceleration
• What is the formula for Newton's Second Law for Rotation?

  $\tau =$$I\alpha$
• The moment of inertia determines how much torque is required for a given angular acceleration.


  True
• In Newton's Second Law for Rotation, the unit for torque (\(\tau\)) is Nm.
• What two factors does moment of inertia depend on?

  Mass and axis of rotation