Define torque and mention its unit.

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Q. Define torque and mention its unit.

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Concept understanding — Torque

What is Torque? The Intuition

Think about opening a door. You push near the handle, not near the hinges. Why? Because the same push is far more effective when applied farther from the hinge. That "turning effectiveness" of a force is exactly what torque measures.

If you push a door with 10 N of force right at the hinge, the door barely moves. Push with the same 10 N at the handle, and it swings open easily. The force is identical — what changed is the distance from the axis of rotation. Torque combines force and distance into one quantity that tells you how much a force will make something spin.

Note

Torque is to rotation what force is to translation. Force makes things move in a straight line; torque makes things rotate.

The Precise Definition

Torque $\vec{\tau}$ about a point (or axis) is defined as the cross product of the position vector $\vec{r}$ (from the axis to the point where force acts) and the force vector $\vec{F}$ :

\vec{\tau} = \vec{r} \times \vec{F}

The magnitude is:

\tau = rF\sin\theta

where $\theta$ is the angle between $\vec{r}$ and $\vec{F}$ .

The direction of torque is given by the right-hand rule: curl your fingers from $\vec{r}$ toward $\vec{F}$ , and your thumb points along $\vec{\tau}$ . This direction is perpendicular to both $\vec{r}$ and $\vec{F}$ .

Tip

For maximum torque, push perpendicular to the lever arm ( $\theta = 90^\circ$ , so $\sin\theta = 1$ ). Pushing directly toward or away from the axis ( $\theta = 0^\circ$ or $180^\circ$ ) produces zero torque — that's why you can't open a door by pushing straight into it.

Why Torque Equals Rate of Change of Angular Momentum

This is the rotational analogue of Newton's second law: $\vec{F} = d\vec{p}/dt$ .

For a particle of mass $m$ at position $\vec{r}$ with velocity $\vec{v}$ , its linear momentum is $\vec{p} = m\vec{v}$ . Angular momentum about the same point is:

\vec{L} = \vec{r} \times \vec{p}

Now differentiate with respect to time:

\frac{d\vec{L}}{dt} = \frac{d\vec{r}}{dt} \times \vec{p} + \vec{r} \times \frac{d\vec{p}}{dt}

Since $d\vec{r}/dt = \vec{v}$ and $\vec{p} = m\vec{v}$ , the first term is $\vec{v} \times m\vec{v} = 0$ (cross product of parallel vectors). The second term uses $d\vec{p}/dt = \vec{F}$ , giving:

\frac{d\vec{L}}{dt} = \vec{r} \times \vec{F} = \vec{\tau}

Important

Net torque equals the rate of change of angular momentum: $\vec{\tau}_{\text{net}} = \frac{d\vec{L}}{dt}$ . This holds for a system of particles as well, provided the torque and angular momentum are taken about the same point.

A Concrete Example

A wrench tightening a bolt. You apply a force of 50 N perpendicular to a wrench that is 0.3 m long. The torque magnitude is:

\tau = (0.3\ \text{m})(50\ \text{N})\sin 90^\circ = 15\ \text{N·m}

If you instead push at a 30° angle, the effective component drops:

\tau = (0.3)(50)\sin 30^\circ = 7.5\ \text{N·m}

Half the torque — you'd need twice the force for the same tightening effect.

Watch out

Torque is a vector, but in many problems you only need its magnitude and sign (clockwise or counterclockwise). Pick a sign convention and stick to it. A common mistake is forgetting that only the perpendicular component of force contributes to torque.

Torque is introduced early in the NCERT Class 11 Physics chapter on System of Particles and Rotational Motion, and 'torque formula τ = r × F' or 'torque important questions class 11 physics' are among the most searched terms for this chapter. The link between torque and rate of change of angular momentum shown here is also a recurring JEE Main derivation-based question.

Step 1. State the definition. Torque (or moment of force) is defined as the moment of an externally applied force about a chosen point or axis of rotation — it measures the force's ability to produce rotational motion.

Step 2. Give the formula. If a force $\vec F$ acts at a point with position vector $\vec r$ relative to the reference point, $\vec\tau=\vec r\times\vec F,\qquad \tau=rF\sin\theta,$ where $\theta$ is the angle between $\vec r$ and $\vec F$ .

Step 3. State the unit. The SI unit of torque is the newton metre (N m). Although this has the same dimensions as energy (the joule), torque is never expressed in joules, since it is a vector describing a turning effect, not a scalar energy.

✓Final answer

\vec\tau=\vec r\times\vec F

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Q.Define torque and mention its unit.

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