6.2 Work and Power in Rotational Motion

• What is the formula for torque in rotational motion?

  \tau = r \times F \sin \theta</latex>
• The angle in the torque formula refers to the angle between the force vector and the lever arm
• Match the characteristic with the correct term:

  Definition of torque ↔️ Measure of rotational force

  Definition of force ↔️ Measure of linear force

  Formula for torque ↔️ $\tau =$$r \times F \sin \theta$

  Formula for force ↔️ $F =$$ma$
• What does torque cause in rotational motion?

  Rotation
• Torque and force have the same units.

  False
• What is the formula for work in rotational motion?

  $W =$$\tau \theta$
• In the work in rotational motion formula, \(\tau\) represents torque
• Steps to derive the equation for work in rotational motion:

  1️⃣ Start with the differential work $dW =$$\tau d\theta$

  2️⃣ Integrate $dW$ over the angular displacement

  3️⃣ Simplify to $W =$$\tau \theta$
• What is the rotational analog of force in linear motion?

  Torque
• The units of work in rotational motion are Newton-meters
• What is the symbol for force in linear motion?

  F
• The work equation in linear motion is W = F ⋅ d
• The unit of work in linear motion is joules (J).

  True
• What is the rotational analog of force in linear motion?

  Torque
• The lever arm length in torque is the distance from the axis to where the force is applied
• The formula for torque is τ = r × F sin θ.


  True
• What is the unit of torque?

  Newton-meter
• Match the characteristic with the correct concept:

  Torque ↔️ Rotational force

  Force ↔️ Linear force
• Torque causes rotation in objects.


  True
• What is the formula for work in rotational motion?

  $W =$$\tau \theta$
• The angular displacement in rotational motion is measured in radians
• The work equation in rotational motion is W = τ ⋅ θ.


  True
• What is the unit of work in rotational motion?

  Newton-meter
• Order the steps to derive the work equation in rotational motion:

  1️⃣ dW = τ dθ

  2️⃣ W = ∫ τ dθ

  3️⃣ W = τ ∫ dθ

  4️⃣ W = τ θ
• What is the formula for power in rotational motion?

  $P =$$\tau \omega$
• The angular velocity in rotational power is measured in radians per second
• The power equation in rotational motion is P = τ ⋅ ω.

  True
• What is the unit of power in rotational motion?

  Watt
• Order the steps to derive the power equation in rotational motion:

  1️⃣ W = τ θ

  2️⃣ P = dW/dt

  3️⃣ P = τ dθ/dt

  4️⃣ P = τ ω
• The formula for work in rotational motion is W = τ θ
• Power is defined as the rate of work done.


  True
• What is the formula for power in rotational motion in terms of torque and angular velocity?

  $P =$$\tau \omega$
• The term $\frac{d\theta}{dt}$ represents the angular velocity
• Power in rotational motion is the product of torque and angular velocity.

  True
• What are the three factors that torque depends on?

  Magnitude, distance, angle
• The formula for torque is \tau = r \times F \sin \theta
• Match the term with its definition:

  Torque ↔️ Rotational force

  Force ↔️ Linear force

  Rotation ↔️ Motion caused by torque

  Linear motion ↔️ Motion caused by force
• What is the formula for work in rotational motion?

  $W =$$\tau \theta$
• The work done in rotational motion is the product of torque and angular displacement.

  True
• The formula for power in rotational motion is P = τ ω