# PHYSICS

A yoyo of mass m=2 kg and moment of inertia ICM=0.09 kg m2 consists of two solid disks of radius R=0.3 m, connected by a central spindle of radius r=0.225 m and negligible mass. A light string is coiled around the central spindle. The yoyo is placed upright on a flat rough surface and the string is pulled with a horizontal force F=24 N, and the yoyo rolls without slipping.

(a) What is the x-component of the acceleration of the center of mass of the yoyo? (in m/s2)

a=

(b) What is the x-component of the friction force? (in N)

f=

Relevant equations: F = ma, torque = I*alpha, a = R*alpha

What I tried to do:

I tried to solve the problem this way:

Using F = ma, and the given, I had F - friction force = ma, with friction force = 22 - 2a. With torque = I*alpha, I got 0.25*friction force - 0.1875*22 = 0.0625*alpha.

To put them all together, I got this equation, R(22-2a) - 0.1875*22 = (0.0625/0.25)*a
And then plugging the given, I got a = 1.83 m/s^2, but I don't think I'm doing this correctly.

Can someone please help me figure out where I went wrong right away. Thanks so much, sorry to be a bother here.

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