What is the Formula for Acceleration in Rotation?

AI Thread Summary
The discussion centers on calculating the acceleration of a body on a rotating wheel with a radius of 10 mm at a frequency of 3 Hz. Key points include the clarification that centripetal acceleration is directed towards the center of rotation and is calculated using the formula a = v^2 / radius. The conversation emphasizes the need to define the coordinate system to accurately determine acceleration in the x, y, and z axes. It is noted that the maximum acceleration occurs when the body is at a specific position on the wheel, and the y component of acceleration may be zero depending on the chosen coordinates. Overall, understanding the relationship between velocity, frequency, and acceleration is crucial for accurate calculations in rotational motion.
Branny12000
Messages
15
Reaction score
0
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
 
Physics news on Phys.org
Branny12000 said:
They just give me one basic equation for acceleration.
You mean centripetal acceleration? It's towards the center.
 
Im not sure I just have 2*pi*freq*distance but I want of course the acceleration in the x y and z directions
 
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?
 
it has normal reaction, centripetal acceleration and angular acceleration above the plane
 
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?
 
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).
 

Similar threads

A Order of rotations due to torque in 3DOF in simulations
Replies
2
Views
1K
B The physics of flywheel launchers (like tennis ball shooters)
2
Replies
60
Views
4K
Exploring Types of Acceleration in Rotational Movement of Rigid Bodies
Replies
33
Views
3K
I Coriolis acceleration of a projectile launched at the equator
Replies
4
Views
2K
I Confused about the axis of rotation in rotational motion w/o slipping
Replies
10
Views
3K
I Solving Wheel Coming to a Stop: FBD, Friction & Hysteresis
Replies
22
Views
4K
Wheel moving in rotation and translation
Replies
15
Views
2K
B Rotational Dynamics: Confused about the tension in this string pulling a mass up an incline
Replies
2
Views
1K
Rotation around a non fixed axis + linear motion of a system
Replies
21
Views
4K
Classical Rotation: Referencing Rotational Motion in Mechanics
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top