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Torque

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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!
Torque Example

What is Torque?

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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.
Torque
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

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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

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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

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A conversion factor is always necessary. Since SI unit of torque is newton meter lets us convert all other units in terms of it:

1 Newton meter = 100 newton centimeter = 1000 newton millimeter = 0.001 kilonewton meter = 100000 dyne meter = 10000000 dyne centimeter = 100000000 dyne millimeter = 0.101971621 kilogram-force meter = 10.19716213 kiloforce centimeter = 101.971621298 kgf mm = 101.971621298 gf m = 10197.162129779 gf cm = 101971.62129779 gf mm = 11.800994078 ozf ft = 141.611928936 ozf in = 0.737562121 lbf ft = 8.850745454 lbf in.

Torque Vs HorsePower

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The torque is the rotational force or twist in the body. Horse power is the measure of the torque rate acting over time. Torque is the turning effort of the engine. The rpm is the rotational speed.
Horse power is used as unit of engine power measurement that determines the engine speed and torque. It is given as

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