If I spin in circles, am I accelerating?

[harp AP 2010]

Homework Statement

If I spin in circles, in place, am I accelerating?

Homework Equations

If acceleration is a change in velocity, which is a vector quantity, does only a change in direction count as acceleration?

The Attempt at a Solution

 

[Dale]

That is an interesting question. Obviously, all of your parts which are not on the axis of rotation have a non-zero velocity which is changing, but your center of mass has a velocity of 0. I would still say that you are accelerating, but I can see the counterargument.

 

[94JZA80]

If I spin in circles, in place, am I accelerating?

yes. as DaleSpam said, there are certainly parts of you that don't fall directly on the axis of rotation, and those parts of you have a non-zero speed that is constantly changing direction. therefore your velocity is constantly changing, i.e. you are accelerating. how to treat the infinitesimal part of you that actually falls directly on the axis of rotation i don't know...

If acceleration is a change in velocity, which is a vector quantity, does only a change in direction count as acceleration?

yes. a velocity is a speed AND a direction - if either or both characteristics are changing, then velocity is changing, and therefore an acceleration is present. think about a turn table spinning a record at constant angular speed. if you choose any random point on the surface of the record (not including its center), it will rotate about the centerpoint at some constant angular speed, depending on its distance from the center. but despite having a constant speed, its direction is NOT constant. in fact its direction is continually changing, and so long as the angular speed of the record remains constant, so does the rate at which the point's direction changes as it rotates about the center of the record. if the rate at which the point's direction changes is constant, then the rate at which velocity changes is also constant, resulting in a constant centripidal acceleration (a constant acceleration toward the center of the record).

many people incorrectly assume that, b/c an object is moving with a constant speed, it must not be accelerating. if the motion is in a straight line, then they are correct in assuming there is no acceleration. but if the constant speed is an angular one (rotating around a centerpoint and therefore constantly changing direction), then the object is accelerating as well.

its easier to see this if you think about the forces associated with accelerations. consider someone driving at a constant 50mph down a straight road. he feels no acceleration, and therefore no force, on his body b/c his velocity is currently constant. if he slams on the gas, the car's velocity begins to change (increase) and he feels the force induced by this acceleration as the car pushes against his back. the force he feels tells him that he is accelerating. now consider centripidal motion (roation around a centerpoint). suppose our driver is driving at a constant 50mph again down a straight road. all of the sudden he turns off the straight road onto a circular road that he can travel around as many times as he wants without having to stop. now despite him maintaining a constant 50mph, the instant he starts turning he feels a force pushing him toward the centerpoint of the of the circular road he's now on. so even though his speed around the circle is constant, his direction is constantly changing. this causes velocity to constantly change, which creates an acceleration (specifically, a centripidal acceleration toward the centerpoint of the circular road), which creates a force that acts toward the centerpoint of the circular road. so even though he's traveling around the circle at a constant speed, his constantly changing direction casues him to feel a centripidal force. if he feels a force, then he knows he's accelerating.