Alexander Fufaev
My name is Alexander FufaeV and here I will explain the following topic:

Torque Simply Explained

Formula

Formula: Newton's 2nd Law of Motion for Rotation
Torque and Angular Acceleration of a Disk
What do the formula symbols mean?

Torque

Unit
Torque describes the rotational effect of a force. It is analogous to the force in linear motion.

Angular acceleration

Unit
Angular acceleration indicates how fast the angular velocity increases per second. The angular acceleration causes the rotation to become faster and faster.

Moment of inertia

Unit
Moment of inertia of a body acts like a resistance to rotation and is analogous to mass in a linear motion.
Explanation

Video

The torque \( \class{green}{\boldsymbol{M}} \) is defined as follows:

Formula anchor

The torque is the cross product of lever-arm length \( \boldsymbol{r} \) and force \( \boldsymbol{F} \).

Because of the cross product the torque vector is always perpendicular to \( \boldsymbol{r} \) and \( \boldsymbol{F} \)! Its magnitude \( |\boldsymbol{r}\times \boldsymbol{F}| = \class{green}{M}\) is the area spanned by the vectors \( \boldsymbol{r} \) and \( \boldsymbol{F} \).

fufaev.org Cross Product of Two Vectors
Cross product of any two vectors \(\boldsymbol{a}\) and \(\boldsymbol{b}\).

The magnitude of the torque, according to the definition of the cross product, is given by the following formula:

Formula anchor

Here \(\varphi\) is the angle enclosed by the vectors \( \boldsymbol{r} \) and \(\boldsymbol{F}\). The torque becomes maximum when the two vectors are orthogonal to each other. So if the angle is \(\varphi = 90^{\circ}\). Formula 2 then simplifies to the product of the force and lever-arm length.

Formula anchor