Find the acceleration of the yo-yo

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To find the acceleration of the yo-yo, the relationship between linear and angular acceleration must be established, where linear acceleration is equal to the radius times angular acceleration (a = rα). The net force acting on the yo-yo can be expressed in terms of tension and gravitational force, while the net torque is related to the tension and the moment of inertia. Solving the torque equation for angular acceleration (α) allows for the calculation of linear acceleration (a). The discussion emphasizes the importance of understanding the dynamics of rigid body motion, including both translation and rotation. Clarifying these relationships will help in determining both the acceleration of the yo-yo and the tension in the string.
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I have calculated the moments of inertia for both the solid disk and the rod, but am getting stuck on how to solve for alpha in the torque equations so that I get acceleration. Can anyone shed some light on this question for me? I really appreciate it.
Here is the question I seem to be struggling with:
A 0.24kg yo-yo consists of two solid disks of radius 11.5cm joined together by a massless rod of radium 1.00cm and a string wrapped around the rod. One end of the string is held fixed and is under constant tension T as the yo-yo is released. Find the acceleration of the yo-yo and the tention T.
 
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i am still stuck on this problem...can anyone help?
 
wildrjetta said:
i am still stuck on this problem...can anyone help?

The in-plane motion of a rigid body consist of a translation of its centre of mass and a rotation around the axis through the center of mass. The linear acceleration is proportional to the net force. The angular acceleration of the rotation is proportional to the net torque. Can you proceed from here?


ehild
 

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