# Simple question about Circular motion

## Homework Statement

When you are spinning an object in a circular path, you are applying centripetal force towards the center of the circle while the velocity vector is perpendicular to it. Therefore the Force component affecting the velocity is FCos(90) = 0. Keeping this in mind, how can you make the object you are spinning move faster or slower?

## Homework Equations

V = rw , w = circuference/Period, F = ma

## The Attempt at a Solution

I am just generally confused by this fact, I tried holding a string and experimenting with it and I can deduce easily that I can change the speed of the circular motion by tightening/letting go a little bit of the string. Yet the question states that this is not possible as the component of the force is FCos(90) = 0 (Which I understand and agree with)

Any help here guys? Any simplifications if possible??

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gneill
Mentor
The question doesn't state what you're allowed to change in order to produce a change in speed. It seems you have a choice of applying a tangential force to the object, thus speeding it up while maintaining the same circular radius, or changing the radius itself as you did.

What conserved quantity of circular (angular) motion involves the radius?

haruspex
Homework Helper
Gold Member
the Force component affecting the velocity is FCos(90) = 0.
That's not quite right. Velocity is a vector, and clearly the force does change the vector. What a constant force at right angles does not change is the speed.
$\ddot {\vec r} = \vec k \times \dot {\vec r}$
$\ddot {\vec r}.\dot {\vec r} = 0$
Integrating
${\dot {\vec r}}^2 = constant^2$
It seems you have a choice of applying a tangential force to the object,
No, I don't think that's the point of the question. As we know, the speed can be changed by a radial force. The question is, how is this possible?
What conserved quantity of circular (angular) motion involves the radius?
And I don't think that solves it either. While it produces the right result, it doesn't resolve the apparent paradox.

My feeling is that it's to do with second order changes. An acceleration does not immediately start changing the position. It changes the velocity, which 'later' changes the position. In the same way, a larger force than that needed to retain circular motion will create a radial acceleration in the sense of $\ddot {|\vec r|}$, i.e. a changing radius (is there another word for this?). This leads to a radial component of velocity, but not instantaneously.

Edit: just realised that $\ddot {|\vec r|}$ is ambiguous. I mean $\frac {d^2}{dt^2} {|\vec r|}$

Last edited:
Chestermiller
Mentor
Is your question "how can I make the object speed up while holding its radial position constant?"

Chet

Stephen Tashi