Introduction

Welcome to the FiveHive article for AP Physics 1: Unit 5.6 - Newton’s 2nd Law in Rotational Form!

In this article, we will go over torque and rotational inertia, as well as drawing parallels to Newton’s second law in linear form. Just like how forces were essential to your understanding of Unit 3, these topics will also be essential to your understanding of the rest of Unit 5.

Torque and Inertia

If you recall Newton’s second law in linear form back in unit 2.5, you might remember that objects accelerate (or change velocity) when the net force applied is not zero. The rotational equivalent of this is that a rotating object’s angular velocity will change when the net torque acting on it is not zero.

Just like how an object accelerates proportionally to the magnitude of the net force acting on it, a spinning object’s angular acceleration is also directly proportional to the net torque acting on it. Furthermore, angular acceleration is inversely proportional to rotational inertia, similarly to how linear acceleration is inversely proportional to mass.Relevant equation:

$\alpha =\frac{\sum \tau }{I}=\frac{{\tau }_{net}}{I}$

$\alpha :\text{Angular acceleration}$

$\tau :\text{Torque}$

$I:\text{Rotational inertia}$

Linear form (for comparison):

$a=\frac{\sum F}{m}=\frac{F_{net}}{m}$

$a:\text{Acceleration}$

$F:\text{Force}$

$m:\text{Mass}$

To describe a rotating system, you may need to use both linear and rotational analyses. For example, a rolling wheel possesses both linear and rotational motion. Rolling motion will further be discussed in 6.5, Rolling.

Practice