- #1
WMDhamnekar
MHB
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- 28
Hi,Klaas van Aarsen said:We are given the angular velocity $\omega = 7\cdot 10^{-5}\,rad/s$ and the mass $M=6\cdot 10^{24}\,kg$.
To achieve a free fall of $0\,m/s^2$ at radius $r$ we need that the centripetal acceleration is equal to the acceleration due to gravity,
Note that $v=\omega r$, so the centripetal acceleration is $\frac{v^2}{r}=\omega^2 r$.
The acceleration due to gravity is $\frac{GM}{r^2}$, where $G=6.67\cdot 10^{-11}$ is the gravitational constant (leaving out the unit while assuming SI units).
So:
$$\omega^2 r = \frac{GM}{r^2}$$
Solve for $r$.
I get the same answer.Dhamnekar Winod said:Hi,
So, we get $r^3 =8.172587755e22m^3/rad^2$ So,$r=43396349.43332m/\sqrt[3]{rad^2}$. Is this answer correct?
Classical mechanics is a branch of physics that deals with the motion of macroscopic objects, such as planets, cars, and baseballs. It describes how these objects move and interact with each other under the influence of forces.
Sir Isaac Newton is considered the father of classical mechanics. He developed the three laws of motion and the law of universal gravitation, which laid the foundation for classical mechanics.
The three laws of motion, as stated by Newton, are:
1. An object will remain at rest or in motion with a constant velocity unless acted upon by an external force.
2. The force acting on an object is equal to its mass multiplied by its acceleration.
3. For every action, there is an equal and opposite reaction.
Classical mechanics deals with the behavior of macroscopic objects, while quantum mechanics describes the behavior of subatomic particles. Classical mechanics follows deterministic laws, while quantum mechanics involves probability and uncertainty.
Classical mechanics has numerous practical applications, including the design of bridges and buildings, the motion of satellites and spacecraft, and the development of vehicles and machines. It is also used in fields such as astronomy, engineering, and sports.