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### Course: Mechanics (Essentials) - Class 11th>Unit 9

Lesson 1: Why do trains stay on track?

# 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.

## Want to join the conversation?

• 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.