How does mass affect angular acceleration?

1 Answer
Jan 20, 2016

Answer:

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.

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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 -= (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#.