# Torque in the rotational form of Newton's second law

The rotational analogue of **force** in translational motion is moment of force, also known as **torque.** It means that just as force does the job in translational motion, a similar job is done by torque in rotational motion. So let us see how force and torque are closely related to each other by their formulae:

First we state the formula which covers up Newton's second law of linear motion:

\[\begin{align} F &= m \cdot a \\ (\text{net external force}) &= (\text{mass}) \cdot(\text{acceleration}). \end{align}\]

However, this law holds for force doing translational motion. Hence, in rotational motion we have a similar equation known as "Newton's second law for rotation." We will now see how they are similar.

Just as Newton's second law of linear motion establishes the relationship between the external net force, mass of the body, and acceleration of body, Newton's second law for rotation establishes the relationship between the external net torque, moment of inertia of the body, and angular acceleration of the body.

Now we state the formula which covers up Newton's second law of rotational motion:

\[\begin{align} \tau &= I \cdot \alpha \\ (\text{net external torque}) &= (\text{moment of inertia}) \cdot(\text{angular acceleration}). \end{align}\]

**Note:** The above product is not a dot product since moment of inertia is tensor quantity.

**Cite as:**Torque in the rotational form of Newton's second law.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/torque-rotational-form-newtons-second-law/