Does a CD's Outer Edge Spin Faster? Math Explained!

[Donna]

My son has asked me a question I cannot answer. Can someone help?

Does any given point on the outer edge of a CD (or any spinning object, like a record album), turn at a faster speed than a given point on the inside edge, because it is going a farther distance in the same amount of time?

What is the math involved?

Thanks.

Donna

 

[whozum]

All points on the CD make the same number of revolutions per unit time, but the linear distance traveled varies with the distance from the center. The outermost part of the CD travels faster than the innermost part.

Linear velocity (speed) = Radius (Distance from center) * Angular velocity (revolutions per unit time)

 

[Fermat]

My son has asked me a question I cannot answer. Can someone help?

Does any given point on the outer edge of a CD (or any spinning object, like a record album), turn at a faster speed than a given point on the inside edge, because it is going a farther distance in the same amount of time?

What is the math involved?

Thanks.

Donna

Yes, the points further from the centre (of rotation) will move faster.

All the points have the same speed of rotation, though. e.g. 33 rpm.

But, the speed of rotation (called the angular velocity) is related to the circumferential speed of the point like this,

v = wr

where v = peripheral velociity
w = angular velocity
r = radius, i.e distance from the centre of rotation.

 

[Galileo]

This question was also answered here:
https://www.physicsforums.com/showthread.php?t=86445