# Vertical rotation movement

## Homework Statement

I have this exercise in physics, that i just don't know how to do.

"A child is spinning a 100g toy, which is attached to a 30cm long rope on a vertical level.
How much force does the rope have to handle?"

Well, the problem for me is, that there's no time given, how long it takes the child to spin it around or speed.

## Homework Equations

a = w^2 * r
w = v/r
w = φ-φo / delta t
w = φ/t
φ = 360 degrees = 2pi

## The Attempt at a Solution

Don't think i can use a = 9.8 m/s^2 for this, to find w and then the other things. Or may be it's just a trick exercise and the solution is just like F = m*a = 0.01m * 9.8m/s^2 = 0.98N?
But then again, the length of the rope should change the force that they toy has on the rope or is that not the case?

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PhanthomJay
Homework Helper
Gold Member
As you noted, the problem statement is incomplete.

As you noted, the problem statement is incomplete.
Yeah, i know, but that's all that i was given. Is it possible then, it's just a trick question and the answer is as simple as F=m*a = 0.98N?

well it could be solved if question question was "what minimum force"

PhanthomJay
Homework Helper
Gold Member
Yeah, i know, but that's all that i was given. Is it possible then, it's just a trick question and the answer is as simple as F=m*a = 0.98N?
No, that would be the tension if the child was just holding the string with the toy dangling down, without spinning it.
well it could be solved if question question was "what minimum force"
Yes it could. It could also be solved if the angular speed was given. But neither was stated in the problem, as written.

but we cant do anything about angular speed ...
all we can do now is to find minimum force

Erm, what's the minimum force then if i may ask, and how do i find it?

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for the minumum force, tension in string at hihgest point should be 0

PhanthomJay
Homework Helper
Gold Member
but we cant do anything about angular speed ...
all we can do now is to find minimum force
You can find the minimum force, but why? the problem states
"How much force does the rope have to handle?"
"I have no idea, unless you tell me what its angular velocity is at a given point. I can tell you what minimum force the rope must handle in order to keep it moving in a circle, but I can't tell you what actual force it is required to handle unless you give me more information". This is an issue when the problem statement is unclear....you waste your time trying to figure out the answer, when there is none.

You can find the minimum force, but why? the problem states
"How much force does the rope have to handle?"
"I have no idea, unless you tell me what its angular velocity is at a given point. I can tell you what minimum force the rope must handle in order to keep it moving in a circle, but I can't tell you what actual force it is required to handle unless you give me more information". This is an issue when the problem statement is unclear....you waste your time trying to figure out the answer, when there is none.
Yes i know, but please tell me anyways, what the minimum force is anyways and how do you find it. Just to know, because this is all the info i have and may be the teacher just specified the question wrongly

I told you already ... ofcourse in any case max force will be at lowest point,

and for that to be minimum, force at highest point should be 0

PhanthomJay
Homework Helper
Gold Member
Yes i know, but please tell me anyways, what the minimum force is anyways and how do you find it. Just to know, because this is all the info i have and may be the teacher just specified the question wrongly
Perhaps the teacher omitted the word 'minimum', in which case it is a good exercise to calculate that minimum force requitred to keep it moving in a circle. Cupid.callin gave you a hint. Now you need to apply Newton's laws, centripetal acceleration concepts, and conservation of energy. Give it a try.

I told you already ... ofcourse in any case max force will be at lowest point,

and for that to be minimum, force at highest point should be 0
English is not my native language, so i have some trouble understanding exactly what it means :(

it's not the words i don't understand, more like content. By lowest point you mean the end of the rope that the child is holding and the highest point, you mean the end of the rope tied to the toy?

PhanthomJay
Homework Helper
Gold Member
Yes i know, but please tell me anyways, what the minimum force is anyways and how do you find it. Just to know, because this is all the info i have and may be the teacher just specified the question wrongly
If you agree that the tension force in the rope must be at least 0 at the top of the circle in order for the toy to move in a circle, then draw a free body diagram of the toy when it is in that position at the top of the circle. Examine the forces acting on it. Since T = 0, there is just one force acting down on it. Identify that force, then use Newton's 2nd law to solve for its centripetal acceleration, which you should be familiar with. This will allow you to find the speed of the toy at the top of the circle. Now find the speed at the bottom of the circle, using conservation of energy. Then look at the forces acting on the toy at the bottom of the circle, and solve for the rope tension using Newton 2 again.

nvn