# How Is Acceleration Calculated for a Freely Falling Yoyo?

• vu10758
In summary: There are other problems involving the string and the yoyo that I could try, but this one doesn't seem to work.In summary, the yoyo is allowed to drop freely with a string held fixed in place at the top. The linear acceleration is 2/3 g and the tension in the string is (1/3)Mg.
vu10758
A yoyo is allowed to drop freely with a string held fixed in place at the top. Assume that the yoyo is a uniform disk of mass M and radius R.

1) Use Newton's Second Law to find the linear acceleration of the yoyo and the tension in the rope.

My answer key says that the answers are 2/3 g for acceleration and (1/3)Mg for tension

I have the net force = ma, and net torque = I*alpha.

so

Net force : mg - T = ma
Net torque = I*alpha

since this is a cylinder

I = (1/2)MR^2

I also know that torque is F*R

I have (1/2)M*R^2*alpha = F*R

F = (1/2)M*R*alpha
Ma = (1/2)M*R*alpha
a =(1/2)*alpha *R

alpha = a/R

so a= (1/2)a

This is not true.

I know how to find tension. I plugged in the correct value for a into the mg-T=ma. But I can't find the acceleration.

Last edited:
Isn't there something else you know about the construction of that yo-yo?

I know that the yoyo is a cylinder that spins counter clockwise going down and clockwise going up. It is attached to a fixed place a tthe top. I don't know what I am missing.

vu10758 said:
I know that the yoyo is a cylinder that spins counter clockwise going down and clockwise going up. It is attached to a fixed place a tthe top. I don't know what I am missing.
Isn't there an inner radius for the axle and an outer radius for the cylinder?

Yes. So I have to include both in the problem. The given R is the outer radius, and the inner radius is not explicitly mentioned.

vu10758 said:
Yes. So I have to include both in the problem. The given R is the outer radius, and the inner radius is not explicitly mentioned.
I don't see how you can do the problem without it. Maybe the problem assumes the string is wound around the outside of the cylinder. If that is the case, then the problem can be done with α = a/R. That is not very realistic for a yo-yo, but it does simplify the calculation.

That is what they assumed to get their answer. I wouldn't call this a yo-yo. It's just a cylinder with a string wrapped around it, but the problem can be done and their answer is OK. I will go back to the first post and look at what you did. You were off to a good start.

vu10758 said:
A yoyo is allowed to drop freely with a string held fixed in place at the top. Assume that the yoyo is a uniform disk of mass M and radius R.

1) Use Newton's Second Law to find the linear acceleration of the yoyo and the tension in the rope.

My answer key says that the answers are 2/3 g for acceleration and (1/3)Mg for tension

I have the net force = ma, and net torque = I*alpha.

so

Net force : mg - T = ma
Net torque = I*alpha

since this is a cylinder

I = (1/2)MR^2

I also know that torque is F*R <== this F is T

I have (1/2)M*R^2*alpha = F*R = T*R

F = (1/2)M*R*alpha = (1/2)M*a = T
Ma = Mg - (1/2)M*R*alpha = Mg - (1/2)M*a
Ma + (1/2)M*a = Mg
(3/2)M*a = Mg
a = (2/3)g
T = (1/2)M*a = (1/2)M*(2/3)g = (1/3)M*g

-----------------------------------------------------------------------------------
a =(1/2)*alpha *R == The rest is replaced ==

alpha = a/R

so a= (1/2)a

This is not true.

I know how to find tension. I plugged in the correct value for a into the mg-T=ma. But I can't find the acceleration.

Sorry if I led you astray. I just didn't get this being a yo-yo problem.

Last edited:

## What is a yoyo?

A yoyo is a toy that consists of a spool attached to a string that is wound around the spool. It is designed to be thrown downwards and then returned to the hand by pulling on the string.

## How do you perform tricks with a yoyo?

Tricks with a yoyo involve manipulating the string and spool to create various movements and patterns. This can include throwing the yoyo in different directions, catching it on different parts of the string, and performing complex string formations.

## Is there a certain type of yoyo that is best for beginners?

There are a variety of yoyo types, including responsive and unresponsive yoyos, that are suited for different skill levels. For beginners, it is recommended to start with a responsive yoyo that is easier to control and return to the hand.

## Can yoyoing be considered a sport?

Yes, yoyoing is considered a sport by many people and has even been recognized by the International Olympic Committee. It requires physical coordination, dexterity, and practice to perform advanced tricks and routines.

## Are there any benefits to playing with a yoyo?

Playing with a yoyo can have several benefits, including improving hand-eye coordination, fine motor skills, and focus. It can also be a fun and engaging form of exercise and stress relief.

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