# Thread: find the equation of motion of a yoyo

1. ## find the equation of motion of a yoyo

A yo-yo consists of two uniform heavy discs, each of mass M and radius R, connected
by a light axle of radius a around which one end of a string is wound. One end of the string is attached to the axle and the other to a fixed point P. The yo-yo is held with its centre of mass vertically below P and then released.

Assuming that the unwound part of the string is approximately vertical, use the principle of conservation of energy to find the equation of motion of the centre of mass of yo-yo. What is the tension of the string when the centre of mass has fallen a distance y?

2. Originally Posted by szpengchao
A yo-yo consists of two uniform heavy discs, each of mass M and radius R, connected
by a light axle of radius a around which one end of a string is wound. One end of the string is attached to the axle and the other to a fixed point P. The yo-yo is held with its centre of mass vertically below P and then released.

Assuming that the unwound part of the string is approximately vertical, use the principle of conservation of energy to find the equation of motion of the centre of mass of yo-yo. What is the tension of the string when the centre of mass has fallen a distance y?
Basic plan of attack:
1. Find the moment of inertia of the yo-yo about an axis of rotation at the point where the string meets the yo-yo.

2. Use conservation of energy. Remember that the CM speed of the yo-yo will be the same as the linear speed that the string unwinds from the yo-yo.

-Dan