Period & Radius of Circular Motion: Equations Explained

[JohnSimpson]

I'm curious, are there any known equations relating the period of a rotating object to the radius of rotation (presumably while under a constant applied force)

What about any relating the applied force to the period?

 

[stunner5000pt]

there is a centripetal acceleration (the acceleration an object while it is moving in a circle, towards the center of the circle)
$$a_{c} = \frac{v^2}{r}$$
the velocity is distance (circumference of the circle) and the time is the period of one rotation
$$v = \frac{2 \pi r}{T}$$
then $$a_[c} = \frac{4 \pi^2 r}{T^2}$$


multiply acceration by force and taht gives the force period relation

 

[quasar987]

multiply acceration by force and taht gives the force period relation

multiply acceration by mass and taht gives the force period relation.

Good analysis stunner !

 

[stunner5000pt]

WELL I am no expert in this field... one can attest to that

 

[marlon]

there is a centripetal acceleration (the acceleration an object while it is moving in a circle, towards the center of the circle)
$$a_{c} = \frac{v^2}{r}$$
the velocity is distance (circumference of the circle) and the time is the period of one rotation
$$v = \frac{2 \pi r}{T}$$
then $$a_[c} = \frac{4 \pi^2 r}{T^2}$$


multiply acceration by force and taht gives the force period relation

And what about the rigid rotators ?

marlon

 

[marlon]

I expected that you'd explain things like "what is a rigid rotator" and "how does the treatement of uniform circular motion made by stunner does not apply to it."

The given treatment only applies to point particles, not massive rotating objects (ie rigid rotators like a spinning sphere or rod)

I'd really like to know who is in your avatar, I assume he is some mathematician or physicist who lived some 235 years ago but I've never seen him before.

Nope, he's not a scientist, he is a far greater genius. You certainly know him.

regards
marlon

 

[hypermonkey2]

Mozart I believe.