What is the Formula for Acceleration in Rotation?

[Branny12000]

Hi there,

I am confused. I want to work out the acceleration that a body placed on a wheel of radius 10 mm going at a frequency of 3Hz would experience in the x y and z axis. The equations for rotation don't make this clear. They just give me one basic equation for acceleration

Can you help me understand this
Bran

 

[A.T.]

They just give me one basic equation for acceleration.

You mean centripetal acceleration? It's towards the center.

 

[Branny12000]

Im not sure I just have 2*pi*freq*distance but I want of course the acceleration in the x y and z directions

 

[mic*]

The instantaneous acceleration is the derivative of the change in velocity per unit time. It is always towards the centre of rotation. So the question, with respect to coordinates, is arbitrary unless you define the problem more clearly.

Ie. at what instant do you wish to know the acceleration, over which chosen layout of coordinates?

 

[Kishlay]

it has normal reaction, centripetal acceleration and angular acceleration above the plane

 

[Branny12000]

Well At x = A So I am guess that the maximum acceleration is 2*pi*freq*distance and in the Y axis it would be when x = A y = 0? so it wouldn't experience maximum acceleration in the y direction?

 

[mic*]

The formula you have stated is for velocity (if distance = radius).
The formula for acceleration is a = v^2 / radius.

If you mean A to be acceleration then, yes, the y component is zero, but technically this means you have chose a coordinate set which does not see the wheel as spinning (because the coordinate turn with the wheel) so frequency = 0 and so will the other results. That is why the term centripetal accelerationis used.

If set the initial position to y = 0, x = 5, with the origin at the centre of the wheel (for example)
you could then calculate the actual position after (t) seconds, and use some pythagorus to get x and y components of the magnitude of centripetal acceleration (that you calculated with the above formula).