Kinematics - Uniform Circular Motion

In summary, the conversation was about finding the period of a satellite's orbit using the gravitational constant and equations for force and acceleration. The attempt at a solution involved using the force equation and angular velocity, but the correct answer is that the period is proportional to R3/2 according to Kepler's Third Law.
  • #1
nahanksh
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0

Homework Statement


What is the period, T, of the satellite's orbit (G is the gravitational constant, 6.7 × 10-11 m3 kg-1 s-2) ?
(The picture is attached)http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam1/sp08/fig18.gif


Homework Equations


a = w^2*r
w=2pi/period
F = -Gm1m2/(R^2)

The Attempt at a Solution



Using the force equation and "a=F/m",

I got a = GMe/Rs^2

And using a = w^2*Rs,

GMe/Rs^2 = w^2*Rs

Then, the angular velocity keeps having Rs^3 which doesn't seem to be right when compared to the answer...

What's wrong with my attempt?
Please help me out here...


The answer should be "T= 2*pi*Rs/sqrt(GMe)
 
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  • #2
nahanksh said:
The answer should be "T= 2*pi*Rs/sqrt(GMe)


No, T should definitely be proportional to R3/2, that's where Kepler's Third Law comes from.
 
  • #3
Oh, so you think what i was doing was right..?
 

1. What is uniform circular motion?

Uniform circular motion is a type of motion where an object moves along a circular path at a constant speed. This means that the object covers equal distances in equal time intervals.

2. How is uniform circular motion different from other types of motion?

Uniform circular motion is different from other types of motion because it involves a constant speed and a change in direction. In other types of motion, the speed and direction may change at different intervals.

3. What is the role of centripetal force in uniform circular motion?

Centripetal force is the force that keeps an object moving in a circular path. In uniform circular motion, the centripetal force is directed towards the center of the circle and is responsible for continuously changing the direction of the object.

4. How do you calculate the speed of an object in uniform circular motion?

The speed of an object in uniform circular motion can be calculated using the formula v = 2πr/T, where v is the speed, r is the radius of the circular path, and T is the time taken to complete one full revolution.

5. Can an object have a constant speed and still be accelerating in uniform circular motion?

Yes, an object can have a constant speed and still be accelerating in uniform circular motion. This is because acceleration is a vector quantity and it includes both the change in speed and the change in direction. In uniform circular motion, although the speed remains constant, the direction of the object is constantly changing, resulting in acceleration.

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