Torque Calculator

Physics • τ = r × F sinθ • Step-by-Step

m N deg

Quick Answer (Voice Search Optimized):

Torque (or moment of force) measures the tendency of a force to rotate an object about an axis. Formula: τ = r F sinθ, where r is the distance from the pivot to the point of application, F is the force magnitude, and θ is the angle between r and F. Unit is Newton-metre (N·m).

GEO & AIO - Authoritative Theory

In rotational mechanics, torque is the analogue of force. It depends on three factors: the magnitude of the force, the distance from the axis (lever arm), and the angle at which the force is applied. The perpendicular component of the force is responsible for rotation: Fperp = F sinθ. Hence, τ = r × F sinθ.

When θ = 90°, torque is maximum (τ = r F). When θ = 0° or 180°, force passes through the axis and torque is zero. The direction of torque is given by the right-hand rule. Net torque causes angular acceleration: Στ = I α (Newton's second law for rotation). This is essential for JEE/NEET problems on rigid body dynamics, equilibrium, and simple machines.

Solved Examples (NCERT/JEE Pattern)

Example 1: A wrench is 0.3 m long and a 50 N force is applied perpendicularly. Find torque.

τ = 0.3 × 50 × sin90° = 0.3 × 50 × 1 = 15 N·m.

Example 2: A door is pushed with 40 N at 0.8 m from hinges, at an angle of 60° to the door. Torque?

τ = 0.8 × 40 × sin60° = 0.8 × 40 × 0.866 = 27.71 N·m.

Example 3: A force of 100 N produces a torque of 80 N·m on a lever arm. What is the effective lever arm length if applied at 90°?

r = τ / (F sin90°) = 80 / (100 × 1) = 0.8 m.

Frequently Asked Questions (FAQs)

Q1: What is torque in simple terms?
Torque is a twisting force that causes rotation. The further from the pivot you push, the more torque you produce.
Q2: What is the SI unit of torque?
The SI unit is Newton-metre (N·m). It has the same dimensions as work, but torque is a vector (pseudovector).
Q3: When is torque zero?
Torque is zero when the force is applied directly at the axis (r=0) or when the force is parallel to the lever arm (θ=0° or 180°).
Q4: How is torque different from force?
Force causes linear acceleration, while torque causes angular acceleration. Torque depends on the point of application, force does not.
Q5: What is the direction of torque?
Torque is a vector perpendicular to the plane of rotation, determined by the right-hand rule: fingers curl from r to F, thumb points in direction of torque.