Many machines employ cams for various purposes, such as opening and closing valv

Question

Many machines employ cams for various purposes, such as opening and closing valves. In the figure below, the cam is a circular disk of radius R with a hole of diameter R cut through it. As shown in the figure, the hole does not pass through the center of the disk. The cam with the hole cut out has mass M. The cam is mounted on a uniform, solid, cylindrical shaft of diameter R and also of mass M. What is the kinetic energy of the cam—shaft combination when it is rotating with angular speed about the shaft's axis? (Use any variable or symbol stated above as necessary.)
K =

Explanation / Answer

Rotational kinetic energy equals I(omega*omega)*0,5, so your major concern is to calculate the moment of inertia of the given system. I(altogether)=I(cam)+I(shaft). You haven' t described the picture enough (off centred?), but I can help you to solve the moment of inertia of your cam, although still not completely. You can consider the cam rupture as if you have a small disc of negative mass, thereby including that the disc is full massed.

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