# Big Yo-Yo problem (Rotational Dynamics with Kinematics? Maybe?)

• ajb13t
In summary, the conversation discussed different approaches to finding translational acceleration and velocity for a yo-yo. The speaker attempted to use the torque equation and energy concepts, but was not successful. Other suggestions were made, including considering the point of space as the origin for torque calculation and determining the moment of inertia. It was also noted that the chosen axis for torque and angular acceleration may affect the calculations.
ajb13t
Homework Statement
A giant yo-yo has a mass of 3 kg and a moment of inertia of 7.68 kg⋅m^2. The central spool has a radius of 0.8 m. As it falls, the string unwinds from the central spool without slipping. If the yo-yo is released from rest, how fast will it be moving when it has fallen a distance of 1.5 meters?
Relevant Equations
## \tau=I\alpha ##
## \tau = r F ##
## x = x_o + vt + 1/2at^2 ##
## (V_ƒ)^2 = (V_o)^2 + 2ax ##
What I attempted to do first was find alpha and turn that into translational acceleration.

Taking mass of yoyo * radius of spool * gravity, (3kg)(0.8m)(9.81m/s^2) yielded 23.544 N*m, and dividing by I = 7.68 kg * m^2 yielded 3.065625 rad/s^2. Finally, multiplying by r = 0.8m gave me 2.4525 m/s^2.

I assumed I could simply use the kinematics equations then, after translating into linear motion, to find velocity at the distance, but every attempt I've made has been wrong. I tried using (Vƒ)^2 = (Vo)^2 + 2ax to give me a velocity, setting vo to 0. But that was incorrect. I also tried some weird thing with [ tex ] x = x_o + v*t + 1/2*a*t^2 [ /tex ] , setting x = 1.5m, x_o = 0, to find t, and using that result again to find v*t. Nothing has worked so far, and I'm not really sure where my thought process is going wrong! Thank you for reading!

Using energy concepts is a good approach to this problem.

If you want to stick with the torque approach, then note the point of space that you are taking to be the origin for your torque calculation. What is the moment of inertia of the yo-yo about this origin?

To elaborate on TSny's reply...
What axis are you taking for the torque and angular acceleration? If centre of spool then the force exerting the torque is the tension in the string, not gravity; if a fixed point in the vertical line of the string then the MoI is not what you used; if the point of contact of spool with string, as a dynamic concept, that is not an inertial frame so may mislead.

## What is the Big Yo-Yo problem?

The Big Yo-Yo problem is a physics problem that involves the rotational dynamics and kinematics of a yo-yo. It requires the application of Newton's laws of motion and conservation of energy to determine the motion of a yo-yo as it is released and falls to the ground.

## What are the key variables in the Big Yo-Yo problem?

The key variables in this problem include the mass of the yo-yo, the radius of the yo-yo, the initial height at which it is released, and the acceleration due to gravity. Other variables such as the angular velocity and tension in the string may also be important depending on the specific problem.

## What are the important equations to solve the Big Yo-Yo problem?

The equations that are typically used to solve the Big Yo-Yo problem include Newton's second law of motion (F=ma), the equation for centripetal force (F=mv^2/r), and the conservation of energy equation (Ei=Ef). These equations can be combined to solve for various unknown variables in the problem.

## What is the difference between rotational dynamics and kinematics?

Rotational dynamics deals with the forces and torques that cause rotational motion, while kinematics focuses on the motion itself without considering the underlying forces. In the Big Yo-Yo problem, rotational dynamics is used to analyze the forces acting on the yo-yo, while kinematics is used to determine its motion and position over time.

## How can the Big Yo-Yo problem be applied in real-life situations?

The principles and equations used in the Big Yo-Yo problem can be applied to various real-life situations, such as analyzing the motion of a spinning top, a yo-yo trick, or the rotation of a planet. It can also be applied in engineering and design, such as in the development of roller coasters or gyroscopes.

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