Velocity Question
 

I just want to verify some thing about velocity. Say we have a spinning disk of radius a. Points of the disk that has the same distance to the center have the same linear velocity right? It travels the circumference of the circle of the chosen radius in a certain time. But different radii's would have different linear velocity. However the angular velocity is the same throughout the entire disk, because it makes the same number of rev/s or else the disk would fly apart some how. Am I correct?

More or less. Remember that linear velocity is composed of both speed and direction. Therefore, although points at the same distance from the center would be moving at the same speed, since they would generally be moving in different directions they would have different velocities. In fact, since speed is determined by distance from the center, and direction of movement is determined by angle from some origin, at a given instant in time every distinct point on the disk would have a different linear velocity.

Angular velocity is just the disk's rate of rotation and therefore is the same at every point on the disk. I'm not totally sure if the center point of the disk is considered to have the same angular velocity as the rest of the disk.

If you got to the <i>very</i> center of the disc, the angular velocity would be zero, because it wouldn't be spinning at all.

Is that true? Just because it's a singularity doesn't mean that it has no angular momentum. It would have no linear velocity, since it's at radiu=0, but I think that it can still have angular velocity

I like this statement. Yes if you had a material that at different distances were to be traveling at different velocities, the material would attempt to shear apart where there is a velocity gradient. Although, if you dig into many materials this may occur. There are few examples that come to mind, CDs will explode at very high RPMs due to the force of the outer extremities of the disc putting excess force on the inner portion. But then you have the wonder idea that a Navy Aircraft carrier will allow about 2.5 revolutions of twist to occur in the shaft from the motor to the prop, meaning until equilibrium is met that there will be slight differences in linear velocity along the path of the shaft.

Oh well... I felt like trying to be smart.

*cheers*

Exactly. Often times the material can withstand the force. However, think of something like pizza dough. As it spins, it changes shape and its diamter increases. Car tires do this as well. Check out those big fat tires on drag cars. They expand an incredible amount.

Yes.....As long as the disk is spinning like a record, and not along another axis.

Oops, you're right. It would still be spinning, but it wouldn't be moving linearly.