UCM - Derive speed, of a body moving, radius r, and the frequency f.

[MohammadG]

Homework Statement

Derive a relationship between the speed v, of a body moving in a circle of radius r, and the frequency f, of the revolutions.

Homework Equations

v=2πr/T
T=1/F

The Attempt at a Solution

Well, I thought this would be as simple as solving for F in the second equations and substituting into the original formula.
Eg:

v=2πr/T
T=1/F
F=1/T

v=2πr/1/F

v=2πr/F

Is the above correct? Could I expand it into more steps, like how one would derive F = 1/T, I already know how to derive v=2πr/T.

Thanks!

 

[PeterO]

Homework Statement

Derive a relationship between the speed v, of a body moving in a circle of radius r, and the frequency f, of the revolutions.

Homework Equations

v=2πr/T
T=1/F

The Attempt at a Solution

Well, I thought this would be as simple as solving for F in the second equations and substituting into the original formula.
Eg:

v=2πr/T
T=1/F
F=1/T

v=2πr/1/F

v=2πr/F

Is the above correct? Could I expand it into more steps, like how one would derive F = 1/T, I already know how to derive v=2πr/T.

Thanks!

Does not the T = 1/f follow from the way they are defined?

Centripetal acceleration is given alternately by mv²/R or 4∏²R/T² which means 4∏²Rf²
by equating the first and last form I think the answer falls out.