Sales Toll Free No: 1-855-666-7446

# Torque

Top
 Sub Topics You could see many physics behind many activities in your daily life like you use a hand crank to raise a bucket of water from the well. To raise the bucket the crank must be applied with enough force.The turning point at which the force applied is what we call torque!

## What is Torque?

A rotational or twisting effect of a force due to the force acting at a distance from the axis of rotation is what we call torque. It is the measure of twist in the object. It is used to measure of the turning force on an object such as bolt or flywheel.

If $\theta$ is the angle between r and F. Torque is defined as
$\tau$ = r $\times$ F = rF sin $\theta$Here r is the length of the lever arm vector or the position vector relative to fulcrum and F is the force vector or force acting on the particle.

The SI unit of torque is Newton meter (Nm) and dimensional formula is [M L2 T -2].

If the force F is perpendicular to radius r then you can eliminate sin $\theta$ then torque $\tau$ = r $\times$ F.

## Torque Equation

Torque is that what decides how much force should act that makes a body to rotate. The object rotates about an axis from a point O we call the force F. The distance from the point O to the point where force acts is the moment arm or the radius of the arm and is denoted as r.
Referring the above figure
A force applied at a distance from the lever arm is its torque. It is given as
$\tau$ = r $\times$ F
Here r is the particles position vector and F is the force applied. The magnitude $\tau$ of the torque is given by
$\tau$ = rF sin $\theta$
Here r is the distance from the axis of rotation to the particle and F is the magnitude of force applied and $\theta$ is the angle between the position and force vectors.

The torque tells about the rate of change of angular momentum L
$\tau$ = $\frac{dL}{dt}$

Here L is the angular momentum and t is the time. If many torques are acting on the body the rate of change of angular momentum is
$\tau_1$ + $\tau_2$ + ....... + $\tau_n$ = $\tau_{net}$ = $\frac{dL}{dt}$

For the rotation about the fixed axis the angular momentum is
L = I $\omega$

Here I is the moment of inertia and $\omega$ is the angular velocity. The net torque is
$\tau_{net}$ = $\frac{dL}{dt}$ = $\frac{d(I \omega)}{dt}$ = I $\alpha$
Here $\alpha$ is the angular acceleration expressed in radian per second square (rad/s2).

## Units of Torque

The SI unit of torque is Newton meter (Nm) or Joule per radian. In imperial and US unit it is measured in foot pounds (ft.lbf), inch pounds or even inch ounces are used.

Here are some common used torque units:

Unit in terms of
Torque Units
dyne
(Metric unit)
dyne Centimeter
 dyne meter dyne millimeter
gram
(Metric unit)
gram force centimeter
 gram force meter gram force millimeter
kilogram
(Metric unit)
kilogram force centimeter
 kilogram force meter kilogram force millimeter kilo newton meter
newton
(Metric unit)
newton centimeter
 newton meter newton millimeter
ounce
(US unit)
ounce force foot
 ounce force inch
pound
(US unit)
pound force foot
 pound force inch

## Torque Conversion

Horse power = $\frac{Torque \times rpm}{5250}$