5.6 Newton’s Second Law in Rotational Form

• Torque is measured in Newton-meters
• What does the moment of inertia quantify?

  Resistance to rotational motion
• What is the unit of moment of inertia?

  kg·m²
• What is angular acceleration defined as?

  Rate of change of angular velocity
• The change in time in the angular acceleration formula is measured in seconds.


  True
• What is angular acceleration defined as?

  Rate of change of angular velocity
• In Newton's Second Law for rotation, τ represents torque
• How is torque defined in rotational motion?

  Product of force and distance
• Match the variable with its definition:

  Moment of Inertia ↔️ Resistance to rotational change

  Torque ↔️ Rotational equivalent of force

  Angular Acceleration ↔️ Rate of change of angular velocity
• The unit of moment of inertia is kg·m²
• What is the symbol for the mass of each particle in the moment of inertia formula?

  m
• What is the unit of angular acceleration?

  rad/s²
• Newton's Second Law in rotational form states that net torque equals moment of inertia times angular acceleration

  True
• What is the angular acceleration of a rotating wheel with a moment of inertia of 2 kg·m² if a net torque of 10 N·m is applied?

  5 rad/s²
• Steps to solve problems using rotational Newton's Second Law:

  1️⃣ Identify the torques

  2️⃣ Calculate net torque

  3️⃣ Determine moment of inertia

  4️⃣ Apply the law: τ = Iα
• The formula for torque is τ = rFsinθ.


  True
• Torque causes an object to rotate about an axis.

  True
• The formula for moment of inertia is I = Σ mr²
• Consider a solid disk of mass 2 kg and radius 0.2 m rotating about its central axis. What is the moment of inertia?

  0.04 kg·m²
• What is the unit of angular acceleration?

  rad/s²
• What is the unit of moment of inertia?

  kg·m²
• What is Newton's Second Law in rotational form?

  τ = Iα
• If a wheel experiences a net torque of 10 N·m and has a moment of inertia of 5 kg·m², its angular acceleration is 2 rad/s²


  True
• If a force of 10 N is applied at a distance of 0.5 m with an angle of 30°, what is the torque?

  2.5 N·m
• The moment of inertia formula is I = Σ mr²
• The formula for moment of inertia is I = Σ mr²
• The formula for angular acceleration is α = (Δω) / Δt
• What is the angular acceleration of an object if its angular velocity changes from 2 rad/s to 6 rad/s in 2 seconds?

  2 rad/s²
• What is the unit of net torque in Newton's Second Law in rotational form?

  N·m
• A force of 10 N applied to a mass of 2 kg results in a linear acceleration of 5 m/s²
• What is the net torque acting on a rod with I = 2 kg·m² and an angular acceleration of 5 rad/s²?

  10 N·m
• What is torque defined as in rotational mechanics?

  Rotational equivalent of force
• If a force of 10 N is applied at a distance of 0.5 m from the axis of rotation with an angle of 30°, what is the torque?

  2.5 N·m
• The moment of inertia depends on the object's mass distribution.

  True
• The formula for angular acceleration is α = (Δω) / Δt
• Angular acceleration is measured in rad/s²
• What does I represent in Newton's Second Law for rotation?

  Moment of inertia
• The formula for torque is τ = rFsinθ
• What is the unit of moment of inertia?

  kg·m²
• Moment of inertia depends on the object's mass distribution relative to the axis of rotation


  True