Angular Acceleration vs Tangential Acceleration

AI Thread Summary
Angular acceleration refers to the change in the angular velocity of an object as a result of torque applied about its center of mass. If a force is applied at a fixed point on a rotating object, it generates angular acceleration without affecting the center of mass if the mass is fixed. However, if the mass is not fixed, both rotational and translational movements occur, resulting in different tangential velocities for various points on the object. The tangential acceleration varies with distance from the axis of rotation, with points further from the center experiencing greater tangential acceleration. Understanding these concepts is crucial for analyzing rotational dynamics accurately.
Telanor
Messages
3
Reaction score
0
Im a little fuzzy on the difference between the two. If you look at the attached picture, if that force stays with the object as it rotates, like a hand pushing in the same spot, would that force cause an angular acceleration?
 

Attachments

  • illistration.JPG
    illistration.JPG
    3.9 KB · Views: 1,217
Physics news on Phys.org
Since the force exerts a torque about the object's center of mass, it will produce an angular acceleration about the center of mass. The force will also produce an acceleration of the object's center of mass.
 
Hey Telanor,

If the mass was fixed where represented by the point in your diagram, then the force will only produce angular accleration, as a constant force will produce acceleration around that point.

If the mass isn't fixed, the mass will exhibit both rotational and translational movement and acceleration.
 
Ok, let's keep things simple. Way more simple. Draw a line on the box. That line will rotate an angle theta as you apply the force. That angle will get bigger and biger as you keep on applying the force. The rate at which that angle gets bigger is the angluar velocity. Same deal for the angular acceleration.

NOW, each point on the body will have a DIFFERENT tangential velocity. It will depend on how far out it is-i.e. the radius. At the very center of rotation, the tangential velocity will be zero. As you move further out, it will increase. This is because it is proportional to radius.

Consider this. All points on the body are rigid. As it sweeps an angle, let's say theta, all the points rotate. But the points on the OUTTER most edge must sweep a BIGGER circle in the same amount of time, hence they must have a higher TANGENTIAL acceleration.
 
If that dot in the center of your diagram represents a fixed axis about which the object is free to rotate (no friction, of course), then it's a much simpler situation. (You didn't mention any fixed axis in your original post.)

In that case the force exerts a constant torque about the center, which produces a constant angular acceleration. The tangential acceleration of each point of the object depends on its distance from the axis: a_t = \alpha r.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
Back
Top