# Acceleration and Circular Motion

Lets assume that there is a force that makes our body moves in circular motion.

We know that the acceleration of a body that moves in circular motion is Velocity ^ 2 / Radius .

How is it possible that if we grant velocity to a body with mass M , Its acceleration is not dependent on M ?

• I'm not completely sure what you are asking. Apr 10, 2014 at 18:50

The definition of acceleration is rate of change of velocity. If you know velocity as a function of time, then you know acceleration. No information concerning mass is required.

Mass and acceleration are two independent variables. You need to consider them together to arrive at a force with the direct relationship F=ma. In other words, if it's mass doubles, so does the force and the acceleration is the same. Gravity works exactly this way.

If you are considering a fixed force from something other than gravity (a force of constant value, independant of mass) then acceleration certainly will be affected by mass. Double mass will be half the acceleration.

You can think of acceleration from a purely mathematical context - it's the rate of change in velocity. (If you're familiar with calculus, you can say that the acceleration is the derivative of velocity.) Because of this, you don't need any mechanics to determine acceleration, so the mass is irrelevant.

More concretely, a mathematician could calculate the acceleration of a point moving in a circle, demonstrating that radial acceleration is independent of mass or any other physical property of the object.

Consider two masses M and m in circular motion with same velocity,v. Both has acceleration v^2/R. The forces acting on the two masses are different. Force will become more on the greater mass. But acceleration of both are same. Because, if you put M and m in the following relation, you get same v^2/R.

$$(mv^2/R)/m=v^2/R$$ since we know $$F/m=a$$ where $$mv^2/R$$ is the centripetal force

also if we want to grant more velocity centripetal force will become more to keep it in circular motion but acceleration expression remains v^2/R with no dependence on mass and increases with increase in velocity.