What I Knew?
I like to challenge myself. I like to learn, so i like to try new things and try to keep growing. -David Schwimmer
This quotation can somewhat summarize what i knew before learning the the topics about Torque, Universal Law of Gravitation and Kepler’s Law of Planetary Motion.
What I Learned?
Let’s talk about Torque!
Torque is a measure of the force that can cause an object to rotate about an axis. Just as force is what causes an object to accelerate in linear kinematics, torque is what causes an object to acquire angular acceleration.
Torque is a vector quantity. The direction of the torque vector depends on the direction of the force on the axis.
For example, when a person opens a door, they push on the side of the door farthest from the hinges. Pushing on the side closest to the hinges requires considerably more force. Although the work done is the same in both cases (the larger force would be applied over a smaller distance) people generally prefer to apply less force, hence the usual location of the door handle.
Torque can be either static or dynamic
A static torque is one which does not produce an angular acceleration. Someone pushing on a closed door is applying a static torque to the door because the door is not rotating about its hinges, despite the force applied. Someone pedaling a bicycle at constant speed is also applying a static torque because they are not accelerating.
The drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track.The terminology used when describing torque can be confusing. The radius at which the force acts is sometimes called the moment arm.
The Equation for torque is:
where, F is the force vector, and r is the vector from the axis of rotation to the point where the force is acting.
The units of torque are force multiplied by distance. The SI unit of torque is the Newton Meter. The most common English unit is the foot-pound.
The Universal Law of Gravitation
There is a popular story that Newton was sitting under an apple tree, an apple fell on his head, and he suddenly thought of the Universal Law of Gravitation.
The Law of Universal Gravitation states that every point mass attracts every other point mass in the universe by a force pointing in a straight line between the centers-of-mass of both points, and this force is proportional to the masses of the objects and inversely proportional to their separation. This attractive force always points inward, from one point to the other.
The Law applies to all objects with masses, big or small. Two big objects can be considered as point-like masses, if the distance between them is very large compared to their sizes or if they are spherically symmetric. For these cases the mass of each object can be represented as a point mass located at its center-of-mass.
Equation which represents Newton’s law of universal gravitation
F = gravitational force of attraction (N)
m1, m2 are the interacting masses (kg)
r is the separation of the masses (m)
G is known as the universal gravitational constant. It sets the strength of the gravitational interaction in the sense that if it were doubled, so would all the gravitational forces.
G = 6.67 ´ 10-11 N m2 kg-2
Every object with a mass in the universe attracts every other according to this law. But the actual size of the force becomes very small for objects very far away. For example, the Sun is about one million times more massive than the Earth, but because it’s so far away, the pull on us from the Sun is dwarfed by the pull on us from the Earth.
As the separation of two objects increases, the separation increases even more, dramatically. The gravitational force will decrease by the same factor (since separation appears in the denominator of the equation).
Weight and the Gravitational Force
We have seen that in the Universal Law of Gravitation the crucial quantity is mass. In popular language mass and weight are often used to mean the same thing; in reality they are related but quite different things. What we commonly call weight is really just the gravitational force exerted on an object of a certain mass. We can illustrate by choosing the Earth as one of the two masses in the previous illustration of the Law of Gravitation:
Thus, the weight of an object of mass m at the surface of the Earth is obtained by multiplying the mass m by the acceleration due to gravity, g, at the surface of the Earth. The acceleration due to gravity is approximately the product of the universal gravitational constant G and the mass of the Earth M, divided by the radius of the Earth, r, squared. (We assume the Earth to be spherical and neglect the radius of the object relative to the radius of the Earth in this discussion.) The measured gravitational acceleration at the Earth’s surface is found to be about 980 cm/second/second.
The inverse square law proposed by Newton suggests that the force of gravity acting between any two objects is inversely proportional to the square of the separation distance between the object’s centers. Altering the separation distance (r) results in an alteration in the force of gravity acting between the objects. Since the two quantities are inversely proportional, an increase in one quantity results in a decrease in the value of the other quantity. That is, an increase in the separation distance causes a decrease in the force of gravity and a decrease in the separation distance causes an increase in the force of gravity.
Furthermore, the factor by which the force of gravity is changed is the square of the factor by which the separation distance is changed. So if the separation distance is doubled (increased by a factor of 2), then the force of gravity is decreased by a factor of four (2 raised to the second power). And if the separation distance (r) is tripled (increased by a factor of 3), then the force of gravity is decreased by a factor of nine (3 raised to the second power). Thinking of the force-distance relationship in this way involves using a mathematical relationship as a guide to thinking about how an alteration in one variable effects the other variable.
The proportionality expressed by Newton’s universal law of gravitation is represented graphically by the following illustration.
In the above figure, the figure on the left hand side indicates the effect of “mass” if the distance between the two objects remains fixed at a given value “d”. The right hand figure shows the effect of changing the distance while keeping the mass constant, and the last part of it shows the effect of changing both the distance and the mass.
Kepler’s Law of Planetary Motion
Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky.
1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.
2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times.
3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semi major axis of its orbit.
Kepler’s laws were derived for orbits around the sun, but they apply to satellite orbits as well.
The Law of Orbits
All planets move in elliptical orbits, with the sun at one focus.
This is one of Kepler’s Law. The elliptical shape of the orbit is a result of the inverse square force of gravity. The eccentricity of the ellipse is greatly exaggerated here.
Orbit Eccentricity
The eccentricity of an ellipse can be defined
as the ratio of the distance
between the foci to the major axis of the ellipse. The eccentricity is zero for a circle. Of the planetary orbits, only Pluto has a large eccentricity
The Law of Areas
A line that connects a planet to the sun sweeps out equal areas in equal times.
 |
This is one of Kepler’s Laws.This empirical law discovered by Kepler arises from conservation of angular momentum. When the planet is closer to the sun, it moves faster, sweeping through a longer path in a given time. |
How I Learned?
Learning new things can be somewhat hard to really understand, sometimes it’s just the matter of time to realize what it is really meant.
Having knowledge about these topics made me “aweee’s and owemgiee” nevertheless it was all a good topic.
For me, the way our teacher explains our lesson has a big impact to better understand the topics, showing us visuals, solving on the board, letting us do some exercises and of course asking us if we understand the lesson.
One way for us to better understand the lesson was our teacher gave us an activity to work on
In this activity we are task to draw and make our own planet. And solved the semi major axis. And in the drawing we also put labels so that it will be more clearer to understand what part of the orbit is that.
Reflection
The more torque I can come up with, the better.
-Anne Sweeney
The more force it gives the better. We know that torque is a measure of the force that can cause an object to rotate. The first thing that came into my mind was a scenario in school were determination represents torque that in order for us to achieve the goals we want in life there must be determination which will be our step in making our dreams. Torque can also be the sacrifices of our parents for us, for us to be a better person one example is them letting us go to school for our future, for our own benefits.
Resources:
https://www.khanacademy.org/science/physics/torque-angular-momentum/torque-tutorial/a/torque
https://wiki.kidzsearch.com/wiki/Torque
http://tap.iop.org/fields/gravity/401/page_46813.html
http://physics.weber.edu/amiri/physics1010online/WSUonline12w/OnLineCourseMovies/CircularMotion&Gravity/reviewofgravity/ReviewofGravity.html
http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html
https://www.britannica.com/science/Keplers-laws-of-planetary-motion
kisharconado 
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