A yo-yo of mass M has an axle of radius b and a spool of radius R. Its moment of inertia can be taken to be MR2/2 and the thickness of the string can be neglected. The yo-yo is released from rest. (a) What is the tension in the cord as the yo-yo descends and as it ascends

The tension in the cord is

Explanation:

Given:

M = mass

b = radius

R = spool of radius

The equation is:

(eq. 1)

The sum of forces in y:

∑Fy = Mg - T = Ma

Replacing in eq. 1

Explanation:

If we ignore the thickness of the string, then the tension T of the string on the yoyo would cause a torque with a magnitude of Tb. This torque would then generate an angular acceleration according to Newton's 2nd law:

We can substitute angular acceleration as ratio of linear acceleration and spool radius

Therefore

The system has 2 forces, gravity pulling it down and tension force upward. The net force would generate the linear acceleration a

now we can substitute for a into the tension equation

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