Question

How does mass affect angular acceleration?

Answer 1

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=tau/I`...................(1)

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

`implies I prop m`

Substituting in equation (1) above we obtain.

`alpha prop tau/m`
or `alpha prop m^-1`

*Hope this helps.

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
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 -= (d omega)/dt = (d^2theta)/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 and omega`.