(455) HL Torque [IB Physics HL]

Torque Concept

• Torque: rotational equivalent of force

• Applied by forces acting at a distance from a pivot point.

Calculation of Torque

• Torque (τ) equation: τ = F * R * sin(θ)

  • F: applied force (Newtons)

  • R: distance from the axis of rotation (meters)

  • θ: angle between the applied force and R (degrees)

• Special case: if θ = 90°, τ simplifies to τ = F * R

• Units: Torque is measured in Newton-meters (Nm)

Newton's Laws of Motion and Torque

First Law (Inertia)

• An object in motion continues in motion unless acted upon by an external force.

• In rotational terms: rotates at a constant speed with no resultant torque (rotational equilibrium).

Second Law (F = ma)

• Rotational analogue: τ = I * α

  • τ: Torque

  • I: Moment of inertia, calculated as Σ(m * r²) (units: kg·m²)

  • α: Angular acceleration (units: radians/s²)

• Net torque leads to angular acceleration.

Third Law (Action-Reaction)

• For every action, there is an equal and opposite reaction.

• Example: Applying torque on an object results in an equal torque that acts on the person applying it.

Torque Direction

• Determined using the right-hand rule:

  • Curl fingers from radius direction (R) to applied force direction (F)

  • Thumb points in the direction of torque.

Example Problem: Uniform Metal Rod

• Scenario: Rod of length 6 m supported at 5 m from the pivot with weight of 40 N.

  • Support force calculation: F1 * R1 = F2 * R2

    • Here, F1 = weight of rod = 40 N, R1 = 6 m (center of mass = 3 m), F2 = support force, R2 = 5 m

  • Solving gives F2 = 24 N.

• After removing support, rod rotates:

  • Torque = F * R, using distance to center of mass.

  • Calculated torque leads to angular acceleration using τ = I * α.