Particle in uniform circular motion

In summary, the satellite's speed is approximately 8.21 m/s^2 and the time interval for one orbit around Earth is around 2 hours or 7000 seconds. The error in the calculation may have been due to not using units.
  • #1
shreddinglicks
212
6

Homework Statement



A satellite is orbiting 600km above the Earths surface. The free fall speed is 8.21 m/s^2. The radius of Earth is 6400km.

What is the satellites speed, and the time interval for one orbit around Earth.

Homework Equations



v = ((2)(PI)(r))/T
ac = rw^2
w = (2)(PI) / T

The Attempt at a Solution



8.21 = 7000w^2
w = .0346

.0346 = (2(PI)) / T
T = .76

(2)(PI)(7000) / .76 = 57871.44

I am unsure of what to do or where I went wrong.
 
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  • #2
You should always use units in your calculations. In this case, units would have shown you where the error is.
(The result should be somewhere around 2 hours or ~7000 seconds, probably a bit less)
 

1. What is a particle in uniform circular motion?

A particle in uniform circular motion is an object that moves in a circular path at a constant speed. This means that the particle covers equal distances in equal amounts of time, and its velocity remains constant throughout the motion.

2. What is the centripetal force in a particle in uniform circular motion?

The centripetal force is the force that keeps a particle in uniform circular motion moving in a circular path. It is directed towards the center of the circle and is responsible for continuously changing the direction of the particle's velocity.

3. How is the centripetal force related to the speed and radius of a particle in uniform circular motion?

The centripetal force is directly proportional to the square of the speed of the particle and inversely proportional to the radius of the circle. This means that as the speed of the particle increases or the radius decreases, the centripetal force also increases.

4. What happens to the centripetal force if the particle's speed or radius changes?

If the speed or radius of the particle in uniform circular motion changes, the centripetal force also changes accordingly. If the speed increases, the centripetal force must also increase to keep the particle in a circular path. Similarly, if the radius decreases, the centripetal force must increase to maintain the particle's circular motion.

5. Can a particle in uniform circular motion experience a net force?

Yes, a particle in uniform circular motion can experience a net force. The centripetal force is always present in a particle's circular motion, but there may be other forces acting on the particle that are not directed towards the center of the circle. In this case, the net force will affect the particle's speed or direction of motion.

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