Merry-Go Round

 Merry-go-rounds are simple machines consisting of round platform and a hopefully frictionless  (to have the most fun) vertical axle. 

http://www.playkids.com/daycare/merrygoround.htm

Physics concepts such as moment of inertia and rotational kinetic energy pertain to this simple concentration of fun.

            The moment of inertia is the constant of proportionality mr², where m is mass, and r is the radius.   The moment of inertia is also called “rotational inertia,” and it identifies a characteristic resistance of moving rotating systems.

            Rotational kinetic energy is the kinetic energy of an object rotating about an axis.  The expression used to find rotational kinetic energy is , where ω equals angular speed, and (the moment of inertia of the object). 

Below is an example of physics being applied to a merry-go-round:

Diameter: 8ft = 2.4384m

Weight 460lbs = 171.69kg

What is the moment of inertia for the merry-go-round?

            I = ½ MR²

            I = ½ (171.69)(1.2192)

            I = 104.662 kg*m²

What is the rotational kinetic energy of the merry-go-round if it is moving at 1.5m/s?

            KE_r = ½ Iω²

            KE_r = ½ (104.662)(1.5) ²

            KEr = 117.745 J

* This is all assuming that the merry-go-round is circular, nobody is on it, and the axle is greased up enough for no friction to be between it and the platform.

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