Torque is a turn or twist force acting. Lets have a simply illustration to know that. When we apply the force the door turns on its hinges. Thus a turning effect is produced when we try to open the door. Have you ever tried to do so by applying the force near the hinge?

In the first case, we are able to open the door with ease. In the second case, we have to apply much more force to cause the same turning effect. What is the reason?

In the first case, we are able to open the door with ease. In the second case, we have to apply much more force to cause the same turning effect. What is the reason?

This turning effect produced by a force on a rigid body about a point, pivot or fulcrum is called the moment of a force or **Torque**.

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Calculate Torque | horsepower calculator from torque |

Torque is the turning effect of the force about the axis of rotation. The moment of force is called **Torque**. It is Rotational analogous of Force.

The Rate at which there is a change in angular momentum is also called** Torque**. It can also be defined as a twist to an object.

When we multiply the magnitude of force or the force's magnitude and the perpendicular distance of the line of action of the force from the axis of rotation then we get a quantity which is called **Torque.**

Mathematically, it can be defined as:

= r F sin$\theta$.

where,

r = a distance between the point from which torque is measured to the point where force is applied.

$\tau$ is the torque and

F = force applied

Its dimensional formula is Consider a rigid body which is rotating about a given axis of rotation on which force is applied. Let us choose an origin **"O"** and let** "r"** be the position vector of the particle on which the force is applied.

Consideration a rigid body, which is rotating about a given axis of rotation**AB** as shown in figure.

Consideration a rigid body, which is rotating about a given axis of rotation

Let

The torque of

To calculate it, we should find the vector

The torque of

O' P $\times$ F = (O'O+OP) $\times$ F

= O'O $\times$ F + OP $\times$ F ..................(a)

As this term will have no component along AB. Thus, the component of O'P $\times$ F is equal to that of O'P $\times$ F

Also, $\tau$ = $\frac{dL}{dt}$

which is the rate of change of angular momentum. This torque mentioned here is basically the net torque, i.e.,

$\tau_{1}$ + $\tau_{2}$ + $\tau_{3}$ + $\tau_{4}$ + so on = $\frac{dL}{dt}$

Hence,

$\tau_{net}$ = $\frac{dL}{dt}$ = $\frac{d( I \alpha )}{dt}$

= I $\frac{d \alpha}{dt}$

= I $\alpha$

$\tau$ = I $\alpha$ ........................(c)Where,

This is called

r = radius, p = momentum L = r $\times$ p ...............(d)

Differentiating the above cross product we get $\frac{dL}{dT}$ = r $\times$ $\frac{dp}{d T}$ + $\frac{dr}{dT}$ $\times$ p

This is due to product rule of differentiation. $\frac{d L}{dT}$ = r x m $\frac{d v}{d T}$ + $\frac{dr}{dT}$ $\times$ m V0) $\frac{dL}{dt}$ = r $\times$ F

$\frac{dL}{dt}$ = $\tau$ ...........................(e)

Torque's dimensional formula is** [M L**^{2} T^{–2}], same as that of work.

According to the formula the S.I unit of torque should be**Newton meter (N-m).**

Other units include :**Nm** but it does not mean both both the quantities are same.

According to the formula the S.I unit of torque should be

Other units include :

- Pound-force-feet (lbf·ft)
- Foot-pounds-force
- Inch-pounds-force
- Ounce-force-inches (oz·in)
- Meter-kilograms-force: S.I unit

A conversion factor is always necessary.

**$Power$ = $Torque \times 2 \pi \times Rotational\ speed$.**

Now, let us add units,

$Power(W)$ = $Torque(N-m)\times 2\pi\times Rotational\ speed(rps)$

On dividing the left by 60 seconds per minute and by 1000 watts per kilowatt we get the following:

**$Power(W)$ =** $\frac{Torque(N.m)\times 2\pi\times Rotational\ speed(rpm)}{60,000}$.

Here, rotational speed is in revolutions per minute (rpm). American automotive engineers sometimes use horsepower for power, foot-pounds (lbf·ft) for torque and rpm for rotational speed. Hence the formula changes to,

**$Power(hp)$ = **$\frac{Torque(ldf.ft) \times 2\pi\times Rotational\ speed(rpm)}{33,000}$

Now, let us add units,

$Power(W)$ = $Torque(N-m)\times 2\pi\times Rotational\ speed(rps)$

On dividing the left by 60 seconds per minute and by 1000 watts per kilowatt we get the following:

Here, rotational speed is in revolutions per minute (rpm). American automotive engineers sometimes use horsepower for power, foot-pounds (lbf·ft) for torque and rpm for rotational speed. Hence the formula changes to,

The differences between Torque and Horsepower are:

Torque is force multiplied by displacement while Horsepower is the unit of power. Torque is measured in**Newton meter** (N-m) while Horsepower is itself a unit of energy denoted by hp and is equal to 745.7 k w.

Torque is calculated as

**$\tau$ = r x F**

While Horsepower is calculated as:

Torque can be calculated as:**Torque **and **Horsepower**.

Torque is force multiplied by displacement while Horsepower is the unit of power. Torque is measured in

Torque is calculated as

While Horsepower is calculated as:

Horse Power = $\frac{\tau \times\ R p m} {5252}$

Torque can be calculated as:

$\tau$ = $\frac{Horse\ power \times 5252}{R p m}$

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