# sphere rolling down an incline plane pulling a rope off a cylinder

The tension in the rope is actually being provided by a solid sphere with radius 23.5 cm that rolls down an incline as shown in the figure. The incline makes an angle of 32° with the vertical. The end of the rope is attached to a yoke that runs through the center of the sphere, parallel to the slope. The friction between the incline and the ball is sufficient that the ball rolls without slipping. The mass of the sphere is closest to

I solved for the Tension in a previous problem to be T= 12.7 N

also angular acceleration of the cylinder is 12.5 rad/s^2 and its mass is 7.25 kg and its radius is 28cm.

I drew some free body diagrams and got

M=2T/((gsin(theta)-(7/5)R(angular acceleration of sphere)) and theta = 58 degrees…..I just dont know how to get the angular acceleration of the sphere.

I tried to get it by equating the torques of the cylinder and sphere but then I needed the mass which is what I am solving for.

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