# How does mass affect angular acceleration?

Jan 20, 2016

Angular acceleration is inversely proportional to mass.

#### Explanation:

For rotational motion, adapting Newton's second law to describe the relation between torque and angular acceleration:

$\tau = I . \alpha$ ,

where $\tau$ is the total torque exerted on the body, and $I$ is the mass moment of inertia of the body.
This can also be written as
$\alpha = \frac{\tau}{I}$...................(1)

We know that Moment of inertia $I$of regular body is given as
$I = m {r}^{2}$ where $m$ is its mass and $r$, is the radius of the circular path of rotation.

$\implies I \propto m$

Substituting in equation (1) above we obtain.

$\alpha \propto \frac{\tau}{m}$
or $\alpha \propto {m}^{-} 1$

*Hope this helps.

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For sake of completeness.

Angular acceleration is the rate of change of angular velocity and is denoted as $\alpha$.

This can be defined either as:
$\alpha \equiv \frac{d \omega}{\mathrm{dt}} = \frac{{d}^{2} \theta}{\mathrm{dt}} ^ 2$, or as

$\alpha = {a}_{T} / r$ ,

where $\omega$ is the angular velocity, ${a}_{T}$ is the linear tangential acceleration, and $r$, is the radius of the circular path in which a point rotates or distance of the rotating point from origin of coordinate system which defines $\theta \mathmr{and} \omega$.