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- Homework Statement
- A space station has the form of a hoop of

radius R = 15 m, with mass M = 1000 kg.

Initially its center of mass is not moving, but

it is spinning with angular speed ωi = 4 rad/s.

A small package of mass m = 19 kg is thrown

at high velocity by a spring-loaded gun at an

angle θ = 19 ◦

toward a nearby spacecraft

as shown. The package has a speed v =

310 m/s after launch. What is the space

station’s rotational speed ωf after the launch?

You may ignore the mass of the package in

calculating the moment of inertia of the space

station.

Answer in units of rad/s.

- Relevant Equations
- Conservation of angular momentum: Lf=Li

Rotational angular momentum: Iω

Translational angular momentum: mvrsinθ

Li = Lrf +Ltf

Iωo = Iωf + mvRsinθ

I = MR^2

(MR^2)ωo = (MR^2)ωf + mvRsinθ

ωf = (MR^2ωo -mvRsinθ)/MR^2 = 3.99

Iωo = Iωf + mvRsinθ

I = MR^2

(MR^2)ωo = (MR^2)ωf + mvRsinθ

ωf = (MR^2ωo -mvRsinθ)/MR^2 = 3.99