5.5 Rotational Equilibrium and Newton’s First Law in Rotational Form

• Newton's First Law in rotational form states that an object rotating with a constant angular velocity will continue to do so unless acted upon by an external torque.


  True
• Rotational equilibrium occurs when no unbalanced torques act on an object.
• What external torque slows down a bicycle wheel spinning at a constant speed?

  Friction
• What is torque calculated as?

  Force times lever arm
• Torque is the rotational equivalent of linear force
• The primary condition for rotational equilibrium is that the net torque on the object must equal zero.


  True
• An external torque is necessary to change rotational motion according to Newton's First Law in rotational form.


  True
• How is torque calculated?

  Force times lever arm
• The net torque on an object is the sum of all individual torques.


  True
• What is the net torque acting on a door in rotational equilibrium on its hinges?

  Zero
• A 4 meter seesaw is balanced in the center. A 60 kg person sits 1.5 meters from the center. How far from the center must a 40 kg person sit to balance the seesaw?

  2.25 meters
• What is the primary condition for rotational equilibrium?

  Net torque equals zero
• Match the aspect with its description:

  Constant Angular Velocity ↔️ Rotational motion remains unchanged

  External Torque ↔️ Necessary to change rotational motion

  Inertia ↔️ Resistance to changes in rotational motion
• What is the significance of zero net torque in rotational equilibrium?

  No unbalanced rotational forces
• The condition for rotational equilibrium is that the net torque acting on the object must equal zero.
• A balanced seesaw with equal torques in opposite directions demonstrates rotational equilibrium.


  True
• Rotational equilibrium occurs when the net torque on an object is zero.


  True
• What does no angular acceleration imply in rotational equilibrium?

  Constant angular velocity
• What is the net torque required for rotational equilibrium?

  Zero
• The net torque in the net torque equation is the sum of all individual torques.


  True
• In rotational equilibrium, the net torque is equal to zero
• Applying the net torque equation can solve for unknown forces or angular acceleration.


  True
• Steps to solve the seesaw problem in Example 2:

  1️⃣ Define key variables

  2️⃣ Set up the torque equation

  3️⃣ Solve for the unknown distance
• Examples of rotational equilibrium include a door balanced on its hinges
• What is an example of an external torque slowing down a spinning bicycle wheel?

  Friction
• An object rotating with a constant angular velocity will continue to do so unless acted upon by an external torque.


  True
• Match the condition with its description:

  Zero Net Torque ↔️ No unbalanced rotational forces

  No Angular Acceleration ↔️ No change in angular velocity
• If the sum of torques is zero, the object is in rotational equilibrium.
• What happens to an object if the sum of torques acting on it is not zero?

  Angular acceleration
• Newton's First Law in rotational form states that an object rotating with a constant angular velocity will continue to do so unless acted upon by an external torque
• Order the conditions for rotational equilibrium based on their descriptions:

  1️⃣ Zero Net Torque

  2️⃣ No Angular Acceleration

  3️⃣ Stationary or Constant Angular Velocity
• What does $\tau_{net}$ represent in the net torque equation?


  Net torque
• Match the condition with its net torque and angular acceleration:

  Rotational Equilibrium ↔️ $\tau_{net} =$$0$ and 0

  Non-Equilibrium ↔️ $\tau_{net} \neq 0$ and ≠ 0
• The torque equation for rotational equilibrium is $\tau_{net} =$$\tau_{1} +$$\tau_{2} =$ 0
• In translational equilibrium, the net force acting on an object must be zero.


  True