Analyzing the Motion of a Released Yoyo: Calculating Acceleration and Tension

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The discussion focuses on calculating the motion parameters of a released yoyo, including linear and angular acceleration, weight, tension in the rope, and angular speed after unwinding. Key equations for these calculations are provided, but the user reports difficulties in obtaining correct results. The lack of access to the referenced figure is noted as a potential issue in solving the problem. Participants are encouraged to clarify the derivation of the equations to identify errors. Accurate calculations depend on properly applying the physics principles related to rotational motion and tension.
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Homework Statement


A yoyo with a mass of m = 179 g is released from rest as shown in the figure.

https://s6.lite.msu.edu/res/msu/nagytibo/Mechanics/Rotation/Graphics/001a.gif"

The inner radius of the yoyo is r = 2.60 cm, and the outer radius is R = 3.60 cm, and the moment of inertia about the axis perpendicular to the plane of the yoyo and passing through the center of mass is ICM = 9.70×10-5 kgm2.
1.Determine the linear acceleration of the yoyo.
2. Determine the angular acceleration of the yoyo.
3.What is the weight of the yoyo?
4.What is the tension in the rope?
5.If a 1.04 m long section of the rope unwinds from the yoyo, then what will be the angular speed of the yoyo?

Homework Equations



These are the equations I believe to be correct. However, they are not working out.
1) a = g*[1 - I/(mr²+I)]
2) α = a/r
3) W = m*g
4) T = g*I*m/(mr²+I)
5) w = v/r = √(2ay)/r


The Attempt at a Solution

 
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The figure is not accessible to us. Also, please show how you got the equations that you believe to be correct, then we might be able to point out where you went wrong.
 

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