centripetal force - The relationship between velocity and radius - Physics Stack Exchange
The time for one revolution around the circle is referred to as the period and denoted the rotational frequency in revolutions per minute or revolutions per second. The acceleration of gravity depends upon the mass of the object which is at The equation expressing the relationship between these variables is derived by. There isn't any relation between time and mass in speical relativity: mass is a Lorentz .. relation that relates imaginary time to physical oscillations (frequency) . Mass, velocity, and radius are all related when you calculate centripetal force. In fact, when you know this information, you can use physics equations to.
Now, what about frequency? Well, frequency literally is the reciprocal of the period. So frequency is equal to one over, let me write that one a little bit neater, one over the period. And one way to think about it is well, how many cycles can you complete in a second? Period is how many seconds does it take to complete a cycle, while frequency is how many cycles can you do in a second?
So, for example, if I can do two cycles in a second, one second, two seconds, three seconds, then my frequency is two cycles per second.
Angular frequency - Wikipedia
And the unit for frequency is, sometimes you'll hear people say just per second, so the unit, sometimes you'll see people just say an inverse second like that, or sometimes they'll use the shorthand Hz, which stands for Hertz.
And Hertz is sometimes substituted with cycles per second. So this you could view as seconds or even seconds per cycle.
- Connecting period and frequency to angular velocity
- Angular frequency
And this is cycles per second. Now with that out of the way, let's see if we can connect these ideas to the magnitude of angular velocity. So let's just think about a couple of scenarios. Let's say that the magnitude of our angular velocity, let's say it is pi radians, pi radians per second.
So if we knew that, what is the period going to be? Pause this video and see if you can figure that out. So let's work through it together. So, this ball is going to move through pi radians every second. So how long is it going to take for it to complete two pi radians? Well, if it's going pi radians per second, it's gonna take it two seconds to go two pi radians.Connecting period and frequency to angular velocity - AP Physics 1 - Khan Academy
And so, the period here, let me write it, the period here is going to be equal to two seconds. Now, I kind of did that intuitively, but how did I actually manipulate the omega here? Well, one way to think about it, the period, I said, look, in order to complete one entire rotation, I have to complete two pi radians. So that is one entire cycle is going to be two pi radians. And then I'm gonna divide it by how fast, what my angular velocity is going to be.
So I'm gonna divide it by, in this case I'm gonna divide it by pi radians, pi, and I could write it out pi radians per second. I'm saying how far do I have to go to complete a cycle and that I'm dividing it by how fast I am going through the angles. And that's where I got the two seconds from.
And so, already you can think of a formula that connects period and angular velocity. Period is equal to, remember, two pi radians is an entire cycle. Newton's Law of Universal Gravitation Orbiting satellites are simply projectiles - objects upon which the only force is gravity. The force which governs their motion is the force of gravitational attraction to the object which is at the center of their orbit.
Planets orbit the sun as a result of the gravitational force of attraction to the sun. Natural moons orbit planets as a result of the gravitational force of attraction to the planet. Gravitation is a force which acts over large distances in such a manner that any two objects with mass will attract.
Newton was the first to propose a theory to describe this universal mass attraction and to express it mathematically. The law, known as the law of universal gravitation states that the force of gravitational attraction is directly proportional to the product of the masses and inversely proportional to the square of the separation distance between their centers.
The value of G is 6. Acceleration of Gravity Since orbiting satellites are acted upon solely by the force of gravity, their acceleration is the acceleration due to gravity g. On earth's surface, this value was 9. For locations other than Earth's surface, there is a need for an equation which expresses g in terms of relevant variables. The acceleration of gravity depends upon the mass of the object which is at the center of the orbit Mcentral and the separation distance from that object d.
The equation which relates these two variables to the acceleration of gravity is derived from Newton's law of universal gravitation. Orbital Speed The speed required of a satellite to remain in an orbit about a central body planet, sun, other star, etc. The equation expressing the relationship between these variables is derived by combining circular motion definitions of acceleration with Newton's law of universal gravitation.
Mechanics: Circular Motion and Gravitation
In the case of an orbiting satellite, this equation for speed can be equated with the equation for the orbital speed derived from universal gravitation to derive a new equation for orbital period. Expressed in this manner, the equation shows that the ratio of period squared to the radius cubed for any satellite that is orbiting a central body is the same regardless of the nature of the satellite or the radius of its orbit.
This ratio is only dependent upon the mass of the object which pulls the orbiting satellite inward. This principle is consistent with as Kepler's third law of planetary motion.
Summary of Mathematical Formulas One difficulty a student may encounter in this problem set is the confusion as to which formula to use. The table below provides a useful summary of the formulas pertaining to circular motion and satellite motion. In the table, many of the formulas were derived from other equations.