# Drawing a FBD of a Stone In Vertical Circular Motion

• tahayassen

## Homework Statement

A stone is tied to a rope. The rope is spun vertically clockwise in circular motion. The rope has a constant speed. Draw four free-body diagrams of the stone when the angle between the rope and the positive x-axis is 0, 90, 180, and 270 degrees.

2. The attempt at a solution

0 degrees (stone is on the right): tension vector to the left, gravity vector pointing down, and centrifugal force pointing down.

90 degrees (stone is at the top): tension vector pointing down, gravity vector pointing down, and centrifugal force pointing right.

180 degrees (stone is on the left): tension vector pointing to the right, gravity vector pointing down, and centrifugal force pointing up.

270 degrees (stone is at the bottom): tension vector pointing up, gravity vector pointing down, and centrifugal force pointing to the left.

Sigh. It's already been 30 seconds since I posted this topic, and still no reply... :( This might take long than expected.

If the stone is spun clockwise it looks to me that at 0 degrees the stone is on the right, 90 degrees the stone is on the bottom, 180 degrees the stone is on the left and 270 degrees the stone is on top.

Sigh. It's already been 30 seconds since I posted this topic, and still no reply... :( This might take long than expected.

Sorry for the delay, the forum site "timed out" after I had just finished typing out my reply - hopefully that won't happen this time.

The first delay, I claimed, was that I had to wait until I had stopped crying at the sight of a physics student referring to centrifugal force. The is no such force. Even you must have had doubts as you had it going in all sorts of directions.

To analyse/identify the forces, let's run through the possibilities.

Firstly the field forces - those weird ones that act without contact.

Gravity - check, you had that one.
Electrostatic - check, they don't apply here so naturally you had none.
Magnetic - check, none of them either.

Now the contact forces:

rigid bodied attached to the stone: [the difficult ones since they can provide a force in just about any direction] - check, there are no rigid bodies attached, so there goes that potential problem.

Strings attached to the stone: [they are much easier to deal with, since you can only pull with a string] - check, you had included that one.

So there you have it: only two forces for each position. Gravity, directed down, and tension directed along the string [to the centre of the circle presumably]

PROBLEM:
If you are attempting to spin a stone in a vertical circle at constant speed, you have to be exceptionally clever with how you hold on to the string.
It is easy with a rigid connection - like the spoke of a wheel - but next to impossible with a string. Indeed, if the string is to have its "other" end fixed at the centre of the circle, the mass will necessarily slow down on the way up one side of the circle, and speed up on the way down the other.

Let's consider the 0o position you dealt with.

The string pulls left [you can only pull with a string]
Gravity pulls straight down.
Combine those two and the net force is angled down.

The only problem is that if this is indeed circular motion at constant speed, the net Force is towards the centre [in the Tension direction]; you need something to balance the gravity [weight] force.
As I implied, if you lift your hand slightly up at just the right time, Tension would be angled up and may "cancel" the weight force. You then have to lower the hand at just the right time/rate so that when the mass was at its low point, it had not dropped too low [beyond the radius of this circle we are aiming at].

It is for this reason that we usually only analyse motion in a vertical circle at exactly the top or exactly the bottom of the circle.

If the stone is spun clockwise it looks to me that at 0 degrees the stone is on the right, 90 degrees the stone is on the bottom, 180 degrees the stone is on the left and 270 degrees the stone is on top.

I'm not sure how it works in Physics, but in Mathematics, positive angles are in the counter-clockwise direction, and negative angels are in the clockwise direction.

Sorry for the delay, the forum site "timed out" after I had just finished typing out my reply - hopefully that won't happen this time.

The first delay, I claimed, was that I had to wait until I had stopped crying at the sight of a physics student referring to centrifugal force. The is no such force. Even you must have had doubts as you had it going in all sorts of directions.

To analyse/identify the forces, let's run through the possibilities.

Firstly the field forces - those weird ones that act without contact.

Gravity - check, you had that one.
Electrostatic - check, they don't apply here so naturally you had none.
Magnetic - check, none of them either.

Now the contact forces:

rigid bodied attached to the stone: [the difficult ones since they can provide a force in just about any direction] - check, there are no rigid bodies attached, so there goes that potential problem.

Strings attached to the stone: [they are much easier to deal with, since you can only pull with a string] - check, you had included that one.

So there you have it: only two forces for each position. Gravity, directed down, and tension directed along the string [to the centre of the circle presumably]

PROBLEM:
If you are attempting to spin a stone in a vertical circle at constant speed, you have to be exceptionally clever with how you hold on to the string.
It is easy with a rigid connection - like the spoke of a wheel - but next to impossible with a string. Indeed, if the string is to have its "other" end fixed at the centre of the circle, the mass will necessarily slow down on the way up one side of the circle, and speed up on the way down the other.

Let's consider the 0o position you dealt with.

The string pulls left [you can only pull with a string]
Gravity pulls straight down.
Combine those two and the net force is angled down.

The only problem is that if this is indeed circular motion at constant speed, the net Force is towards the centre [in the Tension direction]; you need something to balance the gravity [weight] force.
As I implied, if you lift your hand slightly up at just the right time, Tension would be angled up and may "cancel" the weight force. You then have to lower the hand at just the right time/rate so that when the mass was at its low point, it had not dropped too low [beyond the radius of this circle we are aiming at].

It is for this reason that we usually only analyse motion in a vertical circle at exactly the top or exactly the bottom of the circle.

Thank you! This makes so much more sense! I have a question though: when is the centrifugal force used? When it is in a non-inertial or accelerated frame of reference, right? But where is the non-inertial frame of reference in this situtation?

I
Thank you! This makes so much more sense! I have a question though: when is the centrifugal force used? When it is in a non-inertial or accelerated frame of reference, right? But where is the non-inertial frame of reference in this situtation?

Centrifugal Force is used in Chemistry when they explain why the sediment ends up at the bottom of the tube after you put it in a Centrifuge and swich it on. [he says adopting the superior Physics position ]

If anything Centrifugal force is the fictitious force acting in an accelerated frame of reference. The emphasis should be on the word fictitious. There is no such thing really. When an object is traveling in a circle, it is accelerating - otherwise it would go in a straight line. Accelerating can refer to changing the magnitude of your velocity, the direction of your velocity, or a bit of both.

Did you know there are three accelerating "levers" in your car.
The right hand pedal [ called the accelerator in most parts of the world, but the gas pedal in the US]
The middle Pedal [assuming a manual car or the left pedal if the car is automatic]
The round thing in front of the driver.
Only two of them result in acceleration that changes the magnitude of your velocity.

When you stand upright in a street car, and don't adjust for the effects when it brakes heavily, you will fall over. What pushes you over? Answer: Nothing. Or if you are desperate; in the accelerated frame of the accelerating [decelerating] street car, a fictitious force pushed you over. Nothing pushes you over, but unfortunately nothing slows you down either so pretty soon you are traveling faster than the street car.
Same problem when the street car goes around a corner. The street car might be turning left, but you aren't. That means that soon you will be further to the right of the street car. if you move far enough you will contact the side wall - and that wall will then push you to the left.
A passenger is left to wonder "what pushed me over to the side of this street car", and if he asks out loud, any nearby Chemistry student will tell him " it's like being in a centrifuge!" :rofl:

A passenger is left to wonder "what pushed me over to the side of this street car", and if he asks out loud, any nearby Chemistry student will tell him " it's like being in a centrifuge!" :rofl:

XD

Thanks!