Question

If you and your children are on a rotating playground merry-go-round wheel and you jump off, what happens to the rate of spin of he wheel? Assume it has a mass of 200 kg, a radius of 2 meters, and is roughly a disk of solid material initially rotating at 1 turn in 3 seconds. Let your mass be 65 kg and find the new rate of rotation after you jump off.

Answer 1

From given data, radius of gyration is

Initially,

i) Mass of the wheel including the person and children

ii) Speed of rotation of wheel is

Finally,

i) Mass of the wheel along with children excluding the persion is

From conservation of energy, initial energy is equal to the final energy. That is

   ...... (1)

Here are initial and final moment of inertia and are given by and

   are initial and final angular velocities and are given by and

Submit all these in (1)

  

  

submit all the known values,