Torque Calculations to Know for AP Physics 1 (2025)

Torque Vector Formula

τ⃗=r⃗×F⃗, representing the rotational effect of a force about a pivot.

Lever Arm Vector

r⃗, the distance from the pivot to the point of force application.

Force Vector

F⃗, represents the applied force in torque calculations.

Scalar Form of Torque

τ = rF sin(θ), representing the magnitude of torque.

Magnitude of Lever Arm

r, the distance used in the torque formula measured in meters or feet.

Magnitude of Applied Force

F, the force applied measured in Newtons or pounds.

Angle in Torque Formula

θ, the angle between lever arm vector (r⃗) and force vector (F⃗).

Maximum Torque Condition

Occurs when θ = 90°, resulting in τ = rF.

No Torque Condition

Occurs when θ = 0° or 180°, resulting in τ = 0.

SI Unit of Torque

Newton-meters (N·m), the standard unit for measuring torque.

Imperial Unit of Torque

Foot-pounds (ft·lb), an alternative unit for measuring torque.

Net Torque Formula

Στ = τ1 + τ2 + ... + τn, representing the total torque acting on an object.

Sign Convention for Torque

Positive torque indicates counterclockwise rotation; negative torque indicates clockwise rotation.

Equilibrium Condition for Torque

Rotational equilibrium occurs when Στ=0.

Angular Acceleration Relation

Torque is related to angular acceleration as: τ = Iα.

Moment of Inertia (I)

A measure of an object's resistance to rotational acceleration, expressed in kg·m².

Angular Acceleration (α)

The rate of change of angular velocity, measured in rad/s².

Torque due to a Force Sample Problem

Example calculating torque from a 100N force applied at 2m from a hinge.

Torque Calculation Example

τ = rF sin(θ), with given values resulting in τ = 200N·m.

Torque in Equilibrium Sample Problem

Calculating torque from a uniform rod's weight and determining tension in the rope.

Rod's Center of Mass

Located at 1.5 m from the hinge for a 3m long uniform rod.

Torque from Rod's Weight Calculation

Using τW = rW W sin(θ) results in τW = 159.1N·m.

Torque from Rope’s Tension Formula

τT = rT T sin(90°), simplifies to τT = 2T.

Tension Calculation in Equilibrium

Tension found by setting τT equal to τW leading to T = 79.55N.

Resulting Torque from Rod’s Weight

Calculated torque due to the rod’s weight was 159.1N·m.

Resulting Tension in Rope

Tension calculated in the rope holding the system in equilibrium was 79.55N.

Angle for Maximum Torque Production

Maximum torque occurs at an angle of 90° for force application.