(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

See post #3 Assume the YoYo is a solid cylinder with mass M and radius R for all parts!!!!!

2. Relevant equations

Lots?

3. The attempt at a solution

Part A - Find the moment of inertia about the center of mass and the point of contact with the ground:

I_{COM}= 1/2 MR^{2}

I_{IPoC}= 1/2 MR^{2}+ MR^{2}= 3/2 MR^{2}by parallel axis theorem

Part B - Calculate the torque on the Yoyo about the center of mass, and the net horizontal force.

Torque = r x F = rF since r is perp to F

F_{net x}= F cos θ

Part C - What is the angular accel. of the yoyo about its center of mass? Linear acceleration?

Torque = rF = Iα α = rF/I α = 2rF/MR^{2}

and since a_{lin}= αr

a = 2r^{2}F/MR^{2}

Part D - Find the net torque about the instantaneous point of contact

Ok heres where I get stuck. Torque = rF sin σ , where σ is the angle between the applied force F and the r vector, right? Well no joke the geometry is complex. I cant find any way to get the angle between these two, here's what I've got so far:

σ is the angle between the two blue lines, which represent the force and the r vector. Ive also extended the force line so you can see the line of action, if it helps.

Any help would be greatly appreciated!

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# YoYo rolling on ground! (checking work mostly)

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