Solving for Kinetic Energy with Circular Wheel and Weight: Equation Included

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The discussion focuses on calculating the total kinetic energy of a system involving a circular wheel and a falling weight. The moment of inertia of the wheel is defined as I = kmR^2, where k is a constant between 0.5 and 1.0. To find the total kinetic energy, both the rotational kinetic energy and translational kinetic energy must be combined, using the equations E_{k(rotational)} = 1/2 I ω^2 and K = 1/2 mv^2. A follow-up question seeks to determine the speed of the weight after descending a distance h, assuming k=1/2. The conversation emphasizes the importance of including all relevant equations to solve the problem effectively.
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Homework Statement



Consider a circular wheel with a mass m, and a radius R. The moment of inertia about the center of the wheel is I = kmR^2, where k is a constant in the range between 0.5<k<1.0. A rope wraps around the wheel. A weight of mass 2m is attached to the end of this rope. At some moment, the weight is falling with a speed v. The total kinetic energy K of the system at this moment is given by what mathematical equation?

Homework Equations



K = 1/2 mv^2

The Attempt at a Solution



I know that the mass of the wheel will have to be considered to find the final kinetic energy...can someone please give me a hint what to do next?
 
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Use E_{k(rotational)} = \frac{1}{2} I \omega^2, then add the translational kinetic energy term to it. This would give the total kinetic energy. Energy terms in classsical mechanics are hardly ever multiplied or divided, so what's left to do is add or take away. In this case, since it's a total one wants, one adds.
 
Last edited:
thank you so much!
 
V=rw. Net T=T(rotational) + T(translational)
 
How about this?? It's the second part to the question...

Assume that k=1/2

QUESTION...If this system is released from rest, find the speed, v, at the moment when the weight has descended a vertical distance h. Any help would be nice.

Thanks
 
Momentum09 said:

Homework Statement



Consider a circular wheel with a mass m, and a radius R. The moment of inertia about the center of the wheel is I = kmR^2, where k is a constant in the range between 0.5<k<1.0. A rope wraps around the wheel. A weight of mass 2m is attached to the end of this rope. At some moment, the weight is falling with a speed v. The total kinetic energy K of the system at this moment is given by what mathematical equation?

Homework Equations



K = 1/2 mv^2

The Attempt at a Solution



I know that the mass of the wheel will have to be considered to find the final kinetic energy...can someone please give me a hint what to do next?

obviously your relevant equations 2 are incomplete, otherwise you would have your answer... what other relevant equations are there?
 

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