How does mass affect angular acceleration?

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How does mass affect angular acceleration?

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Answer 1 · 2016-01-20T21:51:41

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:

$τ = I . α$ $tau = I.alpha$ ,

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

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

$\Rightarrow I \propto m$ $implies I prop m$

Substituting in equation (1) above we obtain.

$α \propto \frac{τ}{m}$ $alpha prop tau/m$
or $α \propto m^{- 1}$ $alpha prop m^-1$

*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 $α$ $alpha$ .

This can be defined either as:
$α \equiv \frac{d ω}{d t} = \frac{d^{2} θ}{{d t}^{2}}$ $alpha -= (d omega)/dt = (d^2theta)/dt^2$ , or as

$α = \frac{a_{T}}{r}$ $alpha = a_T/r$ ,

where $ω$ $omega$ is the angular velocity, $a_{T}$ $a_T$ is the linear tangential acceleration, and $r$ $r$ , 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 $θ and ω$ $theta and omega$ .

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How does mass affect angular acceleration?

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