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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?

• So Basically (Circumference Equation):

We know that arc length can be in the unit of meters because when we multiply by a radius of 4 meters, we get the linear distance of the arc length.

Now just change displacement for angular velocity:

That will mean that we will get a linear velocity.
Amazing.
• 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.
• arent omega written as Ω
(1 vote)
• Ω is capital or uppercase omega, whereas ω is lowercase omega
(1 vote)
• But here the velocity os V not speed. How did we take V as speed?
• Angular speed is arc length traveled/time (so basically distance), and angular velocity is angular velocity/time. The "v" in this case is linear velocity, while the omega is angular velocity.
(1 vote)
• I don't understand why the magnitude of angular velocity * radius gives the magnitude of velocity. Can someone explain?