Prove a spinning yo-yo has angular velocity

In summary, by conservation of energy, the yo-yo converts its potential energy to rotational energy. This means that the change in potential energy, which is equal to the change in height, is equal to the kinetic energy of rotation, which is equal to 0.5 times the moment of inertia (I) times the angular velocity (w) squared.
  • #1
virgil123
10
0

Homework Statement


Show, by conservation of energy, that when a length, L, of string has unwound that a
yo-yo is spinnning with angular velocity

Remember the yo-yo has both linear and rotational velocity

Homework Equations



[tex]\omega[/tex]= [tex]\sqrt{}[/tex]gL/R[tex]^{2}[/tex]


The Attempt at a Solution


I do not know where to start, any help would be appreciated.
 
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  • #2
The yo-yo converts it's potential energy to rotational energy. So the change in potential potential energy is how much the center of mass has dropped, and by energy conservation that equals the kinetic energy of rotation.

so you need
PE=mgh
Krot=.5 I w^2
 
  • #3
Mindscrape said:
The yo-yo converts it's potential energy to rotational energy. So the change in potential potential energy is how much the center of mass has dropped, and by energy conservation that equals the kinetic energy of rotation.

so you need
PE=mgh
Krot=.5 I w^2

Thank You for your reply.

So am i correct in thinking mgh = 0.5 I w^2
and where the change of height = [gl/r^2], which is the angular velocity, or am I way off the mark??
 

What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed point. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

How is angular velocity different from linear velocity?

Angular velocity measures the rate of change of the angle of rotation, while linear velocity measures the rate of change of the position of an object in a straight line. Angular velocity is also a vector quantity, meaning it has both magnitude and direction, while linear velocity is a scalar quantity with only magnitude.

How can you prove that a spinning yo-yo has angular velocity?

To prove that a spinning yo-yo has angular velocity, you can use the formula v = rω, where v is the linear velocity, r is the radius of the yo-yo, and ω is the angular velocity. You can measure the linear velocity of the yo-yo using a speedometer or radar gun, and then calculate the angular velocity using the formula.

What factors affect the angular velocity of a spinning yo-yo?

The angular velocity of a spinning yo-yo can be affected by the force applied to it, the radius of the yo-yo, and the moment of inertia. The moment of inertia is a measure of an object's resistance to changes in its rotation and is affected by the shape and mass distribution of the yo-yo.

How does the angular velocity of a spinning yo-yo relate to its kinetic energy?

The kinetic energy of a spinning yo-yo is directly proportional to its angular velocity squared. This means that as the angular velocity increases, so does the kinetic energy. This relationship is important in understanding the energy conservation of spinning objects, such as yo-yos.

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