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# Radius comparison from velocity and angular velocity: Worked example

Predicting which spinning disc has a larger radius from angular velocity and the linear velocity of a point on the edge.

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• I'm getting the idea that angular speed is equal to linear speed. So if angular speed equals linear speed because they are the same thing then:
Ang. Speed = Lin. Speed

Ang. Speed = |w|r
Lin. Speed = |v|

And from here:

|w|r = |v|

And so:

|v| = |w|r
|w| = |v|/r
r = |v|/|w|

Also: r in mathematics has a relation to pi as a ratio and determines the magnitude of some triangle formed by and angle theta.

If I remember geometry correctly:

C = 2πr
A(circle) = πr^2

So:

π = C/2r
π = A(circle)/r^2

And:

r = C/2π

Just how:

r = |v|\|w|

My point on this part is that radius involves a ratio-like relationship between the mathematics and physics side of the equation.
(1 vote)
• But here the velocity os V not speed. How did we take V as speed?
• Well, we're talking about the magnitude of velocity here, which is speed.
• Would have been clearer if you wrote Velocity = S/Delta T
Then wrote V = W*R
• A bit confused as to how you can relate angular velocity and velocity to radius. Can't they both be spinning at the exact same speed making it harder to determine the radius?
• Why would it be difficult to determine the radius if they are moving at the same speed? They are two separate values derived from separate things. Angular velocity from the change in angel over time and velocity from the change in displacement over time.
• I don't understand why the magnitude of angular velocity * radius gives the magnitude of velocity. Can someone explain?