A runner of mass 53.0 kg runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude 3.60 m/s . The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.200 rad/s relative to the earth. The radius of the turntable is 2.90 m , and its moment of inertia about the axis of rotation is 76.0 kg⋅m2

0.336 rad/s

Explanation:

= Angular speed of the turntable = -0.2 rad/s

R = Radius of turntable = 2.9 m

I = Moment of inertia of turntable =

M = Mass of turn table = 53 kg

= Magnitude of the runner's velocity relative to the earth  = 3.6 m/s

As the momentum in the system is conserved we have

The angular velocity of the system if the runner comes to rest relative to the turntable which is the required answer is 0.336 rad/s

we're given that v₀ = 0 and a = 5.4 m/s². therefore, since v = at + v₀ for constant acceleration the equation for velocity is

after 28s,

m/s

which i would round to 150 m/s as my final answer

you can cut your hand off if your not