5.2 Torque and Rotational Statics

• The formula for torque is τ = rF\sin\theta
• Torque is a measure of the rotational force acting on an object about a specific axis of rotation.
• The formula for torque is Torque = Force × Distance × sin(Angle)
• The torque formula includes the variable τ, which represents torque.
• Match the variable in the torque formula with its units:

  τ ↔️ N·m

  r ↔️ m

  F ↔️ N

  θ ↔️ degrees
• The larger the lever arm, the greater the torque produced by the same force


  True
• Match the factor in torque calculation with its description:

  Force (F) ↔️ Magnitude of the force applied

  Distance (r) ↔️ Distance from axis to force application

  Angle ($\theta$) ↔️ Angle between force and lever arm
• What is the magnitude of the force applied called in the context of torque?

  Force
• The angle in the torque formula is between the force vector and the lever arm.


  True
• A 10 N force applied 0.5 m from the axis at a 90° angle produces a torque of 5 N·m.
• A force applied directly at the axis of rotation produces no torque.


  True
• The formula for torque is τ = rF \sin(\theta)</latex>.


  True
• The unit of torque is Newton-meters (N·m).
• The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force.

  True
• Why is a greater lever arm more efficient for rotational motion?

  Produces larger torque
• What is the torque produced by a 10 N force applied 0.5 m from the axis at a 90° angle?

  5 N·m
• The formula for calculating torque is τ
• What is the torque produced by a 20 N force applied 0.3 m from the axis at a 30° angle?

  3 N·m
• A 10 N force applied 0.5 m from the axis at a 90° angle produces a torque of 5 N·m.


  True
• The formula for calculating torque is τ
• What is the torque produced by a 20 N force applied 0.3 m from the axis at a 30° angle?

  3 N·m
• Torque is directly proportional to the force, distance from the axis, and the sine of the angle
• Rotational equilibrium requires both net torque and rotational acceleration to be zero.

  True
• One condition for rotational equilibrium is that the net torque equals zero
• No rotational acceleration is a condition for rotational equilibrium.

  True
• For rotational equilibrium, the net torque must be zero.


  True
• No rotational acceleration is a condition for rotational equilibrium.


  True
• Steps to solve statics problems using torque balance:

  1️⃣ Choose a reference point

  2️⃣ Calculate each torque using τ = rFsinθ

  3️⃣ Sum all torques: Στ = 0
• In rotational statics, the net torque must be zero


  True
• The magnitude of the force applied is a factor that affects torque


  True
• Torque causes an object to rotate or twist about an axis


  True
• The unit for torque is Newton-meters (N·m)


  True
• The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force.
• The formula for torque is τ = rF \sin(\theta)
• A force applied directly at the axis of rotation results in no torque


  True
• The distance from the axis of rotation to the point where the force is applied is called the distance
• What is the formula for torque?

  $τ =$$rF \sin(\theta)$
• What is the torque produced by a 20 N force applied 0.3 m from the axis at a 30° angle?

  3 N·m
• What is torque a measure of?

  Rotational force
• The perpendicular distance from the axis of rotation to the line of action of the force is called the lever arm.