Expand each vector into their component forms:

Similarly,


Then assuming the resultant vector
is the sum of these three vectors, we have


and so
has magnitude

and direction
such that

Answer:
20.62361 rad/s
489.81804 J
Explanation:
= Initial moment of inertia = 9.3 kgm²
= Final moment of inertia = 5.1 kgm²
= Initial angular speed = 1.8 rev/s
= Final angular speed
As the angular momentum of the system is conserved

The resulting angular speed of the platform is 20.62361 rad/s
Change in kinetic energy is given by

The change in kinetic energy of the system is 489.81804 J
As the work was done to move the weight in there was an increase in kinetic energy
Answer:
22 N applied force
Explanation: Since they are both pushing the wagon in the same direction the force adds up.
A protostar reaches equilibrium when gravity is balanced by the outward force of nuclear fusion.