Sample:
As soon as the lightning is seen, sound travels in the air for several kilometers until it eventually reaches the observer.
If the period of a satellite is T=24 h = 86400 s that means it is in geostationary orbit around Earth. That means that the force of gravity Fg and the centripetal force Fcp are equal:
Fg=Fcp
m*g=m*(v²/R),
where m is mass, v is the velocity of the satelite and R is the height of the satellite and g=G*(M/r²), where G=6.67*10^-11 m³ kg⁻¹ s⁻², M is the mass of the Earth and r is the distance from the satellite.
Masses cancel out and we have:
G*(M/r²)=v²/R, R=r so:
G*(M/r)=v²
r=G*(M/v²), since v=ωr it means v²=ω²r² and we plug it in,
r=G*(M/ω²r²),
r³=G*(M/ω²), ω=2π/T, it means ω²=4π²/T² and we plug that in:
r³=G*(M/(4π²/T²)), and finally we take the third root to get r:
r=∛{(G*M*T²)/(4π²)}=4.226*10^7 m= 42 260 km which is the height of a geostationary satellite.
Answer:
a) C.M 
b) 
Explanation:
The center of mass "represent the unique point in an object or system which can be used to describe the system's response to external forces and torques"
The center of mass on a two dimensional plane is defined with the following formulas:


Where M represent the sum of all the masses on the system.
And the center of mass C.M 
Part a
represent the masses.
represent the coordinates for the masses with the units on meters.
So we have everything in order to find the center of mass, if we begin with the x coordinate we have:


C.M 
Part b
For this case we have an additional mass
and we know that the resulting new center of mass it at the origin C.M
and we want to find the location for this new particle. Let the coordinates for this new particle given by (a,b)

If we solve for a we got:




And solving for b we got:

So the coordinates for this new particle are:

Answer:
Explanation:
Given
mass of sphere 
diameter of sphere 
radius 

friction will provide resisting torque so
where 







(b)time taken to decrease its rotational speed by 



Well a basic explanation is that some elements have enough electrons to be considered stable. These elements do not need to react with other elements to gain more electrons. Reactive elements are no where near stable; they respond with other elements in order to become stable. The more unstable, the harsher the reaction is.