# Yo-yo problem - rotational motion

• Physics197
In summary, we are considering a yo-yo with R = 3.3 cm, r = 0.3 cm, and mass m = 84 g. We are trying to find the speed of the yo-yo after it has fallen a distance h = 1.20 m, the tension in the string while it falls, and the magnitude of the acceleration of the center of mass. To solve this, we can use the equations L = Iω, I = 0.5MR^2, KEr = 0.5Iω^2, and Tnet = Ia. We can also use conservation of energy and differentiate to find the acceleration. The moment of inertia can be found using the large
Physics197

## Homework Statement

consider a yo-yo with R = 3.3 cm, r = 0.3 cm, and mass m = 84 g.

What is the speed of the yo-yo after it has fallen a distance h = 1.20 m?

What is the tension in the string while the yo-yo falls?

What is the magnitude of the acceleration of the centre of mass as the yo-yo falls?

L = Iw
I = 0.5MR^2
KEr = 0.5Iw^2
Tnet = Ia

## The Attempt at a Solution

change h into rotational displacement, not sure where to go or if that's even right.

can anyone give me direction?

Last edited:
would you solve this using conversation of energy?

Yes, I would use energy for the first part. You have both rotational and translational energy and they are related by v = rω. The r = 0.3 cm must be the radius of the center "axel" that the string unwraps from.

If you don't put in the h = 1.2 too soon, you'll have the speed as a function of h. Perhaps you can differentiate that with respect to time and get something you can use to find the acceleration.

what would the moment of inertia be? 0.5mr^2, would you use the large or small radius?

would the height be 1.2 m? for PE

Yes, the large radius for moment of inertia.
Yes, the initial height is 1.2 m.

## What is the Yo-yo problem in rotational motion?

The Yo-yo problem is a classic problem in physics that involves a yo-yo being released from rest at a certain height and allowed to fall under the influence of gravity while also winding up the string around its center axis. The goal is to determine the tension in the string and the angular velocity of the yo-yo at any given time.

## What are the key assumptions made in the yo-yo problem?

Some key assumptions made in the yo-yo problem include: the string is massless and inextensible, the yo-yo is a solid disk with a constant mass and radius, and there is no slipping or friction between the yo-yo and the surface it is on.

## How is the yo-yo problem solved?

The yo-yo problem can be solved using Newton's second law and the conservation of energy. By setting up equations for the forces and energy involved, the tension in the string and the angular velocity of the yo-yo can be determined at any given time.

## What is the significance of the yo-yo problem?

The yo-yo problem is significant because it demonstrates the application of fundamental principles in rotational motion, such as torque, angular acceleration, and conservation of energy. It also has real-world applications in engineering, such as designing mechanisms for reeling in cables or ropes.

## How does the yo-yo problem relate to other problems in physics?

The yo-yo problem is similar to other problems in physics that involve objects rotating and translating simultaneously, such as a rolling ball or a spinning top. It also has connections to other problems involving tension, such as a hanging mass on a string or a pendulum swinging back and forth.

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