Question

A large wooden turntable in the shape of a flat disk has a radius of 2.45 m and a total mass of 140 kg . The turntable is initially rotating at 3.20 rad/s about a vertical axis through its center. Suddenly, a 68.5 kg parachutist makes a soft landing on the turntable at a point on its outer edge.

Find the angular speed of the turntable after the parachutist lands.(Assume that you can treat the parachutist as a particle.)

Answer 1

Given that ,

Radius of the flat disk = 2.45 m

mass of the disc = 140 Kg

initial rotating speed = 3.20 rad/s

mass of the parachutist = 68.5 Kg

angular speed of the turntable after the parachutist lands??

Moment of inertia of the disc

a 68.5 kg parachutist makes a soft landing on the turntable

after this , the new moment of inertia = I_{d +} I _p

where I_d is the moment of inertia of the disc and I _p is the moment of inertia of the parachute .

Total Moment of inertia = Moment of inertia of the disc+moment of inertia of the parachute

Total moment of inertia =420.14+411.13

= 831.27 Kg m ²

according to conservation of angular momentum ,

When no external torque acts on the body , the initial angular momentum of the rotating body will be equal to the final angular momentum.

  

angular speed of the turntable after the parachutist lands is 3.27 rad/s