# Torque

on . Posted in Classical Mechanics

Torque, abbreviated as $$\tau$$ (Greek symbol tau) or T, also called moment of force, is a type of force that is applied to an object that results in the object rotating around an axis.  It is a measure of how much twisting is applied to an object.

### Torque Index

Force is an action that causes a change in the motion of an object.  Torque also concerns acceleration that is always at an angle.  It is a vector but the direction varies according to the direction of the force that is being applied. The amount of force needed to bring about movement with torque decreases as distance increases from the point of rotation.  Torque in a valve is the amount of rotational force to overcome the resistance of a valve sleeve and line pressure to close the sleeve.

### Torque for perpendicular Force formula

$$\tau \;=\; r \; F$$     (Torque for Perpendicular Force)

$$r \;=\; \tau \;/\; F$$

$$F \;=\; \tau \;/\; r$$

### Solve for r

 torque, τ force, F

### Solve for F

Symbol English Metric
$$\tau$$  (Greek symbol tau) = torque $$lbf-ft$$ $$N-m$$
$$r$$ = radius $$in$$ $$mm$$
$$F$$ = force $$lbf$$ $$N$$

### Torque for Angled Force formula

$$\tau \;=\; r \; F \; sin \; \theta$$     (Torque for Angled Force)

$$r \;=\; \tau \;/\; F \; sin \; \theta$$

$$F \;=\; \tau \;/\; r \; sin \; \theta$$

$$\theta \;=\; \tau \;/\; r \; F$$

### Solve for τ

 radius, r force, F angle, θ

### Solve for r

 torque, τ force, F angle, θ

### Solve for F

 torque, τ radius, r angle, θ

### Solve for θ

 torque, τ radius, r force, F

Symbol English Metric
$$\tau$$  (Greek symbol tau) = torque $$lbf-ft$$ $$N-m$$
$$r$$ = radius $$in$$ $$mm$$
$$F$$ = force $$lbf$$ $$N$$
$$\theta$$  (Greek symbol theta) = angle between force and lever $$deg$$ $$rad$$

### Torque for Angular Acceleration and Moment of Inertia formula

$$\tau \;=\; I \; \alpha$$     (Torque for Angular Acceleration and Moment of Inertia)

$$I \;=\; \tau \;/\; \alpha$$

$$\alpha \;=\; \tau \;/\; I$$

Symbol English Metric
$$\tau$$  (Greek symbol tau) = torque $$lbf-ft$$ $$N-m$$
$$I$$ = moment of inertia $$lbm \;/\; ft^2-sec$$ $$kg \;/\; m^2$$
$$\alpha$$  (Greek symbol alpha) = angular acceleration $$deg \;/\; sec^2$$ $$rad \;/\; s^2$$

### Motor Torque formula

$$\tau \;=\; HP \; 5252 \;/\; S$$     (Motor Torque)

$$HP \;=\; \tau \; S \;/\; 5252$$

$$S \;=\; HP \; 5252 \;/\; \tau$$

Symbol English Metric
$$\tau$$  (Greek symbol tau) = motor torque $$lbf-ft$$ $$N-m$$
$$HP$$ = horsepower $$lbf-ft\;/\;sec$$ $$J\;/\;s$$
$$S$$ = speed $$rpm \;/\; sec$$ $$rpm \;/\; s$$

### Breakaway Torque

The torque necessary to put into reverse rotation a bolt that has not been tightened.