2 dimensional motion consists of projectile motion, circular motion and angular velocity, and gravity and how it affects orbits and other objects.
PROJECTILE MOTION
In projectile motion, the X and Y accelerations and velocity are independent from each other and do not affect each other in any way.
These are some of the equations used in order to calculate different variables in projectile motion equations:
(ax = 0) vx = v0x = v0 cosØ x = x0 + v0xt = x0 + (v0 cos Ø)t - ( these are for the X direction)
(Ay = -g) Vy = v0y + ayt = v0 sin Ø + (-g)t Y = y0 + v0yt + 1/2ayt2 = y0 + (v0 sin Ø)t - ½gt2 - (These are for the Y directions)
When an object is a projectile, the only force acting on it is gravity, so that is the net force. An object with a higher initial velocity than another object will spend more time in the air than an object with a lesser initial velocity. If you fire a projectile at 30° and another object at 60° they will spend the same amount of time in the air and land in the same spot. This is only the case for 30 and 60 degrees. If two objects are projectiles and land at different spots ( one farther than the other ) and they have the same maximum height, you know that the object that went farther had the higher initial velocity.
Circular Motion
Circular motion uses angular acceleration and linear velocity to measure variables. The centripetal acceleration in a circle is always pointed towards the center of the circle. If an object were to stop moving in a circular motion after it had been moving in a circular motion, it would move in a tangent to the last point it was touching the circle. In places like orbits where circular motion is used, the acceleration is always pointed towards the center of the earth and the only force is gravity, which equals the centripetal force and the net force. So the net fore, centripetal force, and the force of gravity are all equal in some occasions. Examples of circular motion are cars going around a corner at high speeds are unstable and unlikely to make it around the corner successfully because they are not gripping the road. On the other hand, cars traveling at a lower speed are much more likely to complete the turn without sliding because they are able to have a higher state of friction. Some equations that would be used are Ac = v^2/r
Gravity
Gravity uses both projectile motion and circular motion in its equations. For gravity there is a universal gravitational constant that is referred to as "G" which is 6.67 x 10^-11. This can be used on anywhere in the universe to find the gravitational field strength as ong as you know the planet's mass and its radius. Some equations that would be used in finding the gravitational field strength of a planet would be: Fg= (G x m1 x m2)/(r^2), where G is the universal gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the radius of the planet, or the distance from the center of the planet to the object your are measuring. Another important part of Gravity is its changing factors. If you have two objects that are 100 grams that are 10 feet apart, they would have a gravitational field strength of "X". If you were to double the mass of one of the objects to 200 grams and keep the distance the same, the gravitational field strength would double. On the other hand, if you were to have them at the same mass, and double the distance between them, the gravitational field strength would be 1/4 of what it was to start with.
In projectile motion, the X and Y accelerations and velocity are independent from each other and do not affect each other in any way.
These are some of the equations used in order to calculate different variables in projectile motion equations:
(ax = 0) vx = v0x = v0 cosØ x = x0 + v0xt = x0 + (v0 cos Ø)t - ( these are for the X direction)
(Ay = -g) Vy = v0y + ayt = v0 sin Ø + (-g)t Y = y0 + v0yt + 1/2ayt2 = y0 + (v0 sin Ø)t - ½gt2 - (These are for the Y directions)
When an object is a projectile, the only force acting on it is gravity, so that is the net force. An object with a higher initial velocity than another object will spend more time in the air than an object with a lesser initial velocity. If you fire a projectile at 30° and another object at 60° they will spend the same amount of time in the air and land in the same spot. This is only the case for 30 and 60 degrees. If two objects are projectiles and land at different spots ( one farther than the other ) and they have the same maximum height, you know that the object that went farther had the higher initial velocity.
Circular Motion
Circular motion uses angular acceleration and linear velocity to measure variables. The centripetal acceleration in a circle is always pointed towards the center of the circle. If an object were to stop moving in a circular motion after it had been moving in a circular motion, it would move in a tangent to the last point it was touching the circle. In places like orbits where circular motion is used, the acceleration is always pointed towards the center of the earth and the only force is gravity, which equals the centripetal force and the net force. So the net fore, centripetal force, and the force of gravity are all equal in some occasions. Examples of circular motion are cars going around a corner at high speeds are unstable and unlikely to make it around the corner successfully because they are not gripping the road. On the other hand, cars traveling at a lower speed are much more likely to complete the turn without sliding because they are able to have a higher state of friction. Some equations that would be used are Ac = v^2/r
Gravity
Gravity uses both projectile motion and circular motion in its equations. For gravity there is a universal gravitational constant that is referred to as "G" which is 6.67 x 10^-11. This can be used on anywhere in the universe to find the gravitational field strength as ong as you know the planet's mass and its radius. Some equations that would be used in finding the gravitational field strength of a planet would be: Fg= (G x m1 x m2)/(r^2), where G is the universal gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the radius of the planet, or the distance from the center of the planet to the object your are measuring. Another important part of Gravity is its changing factors. If you have two objects that are 100 grams that are 10 feet apart, they would have a gravitational field strength of "X". If you were to double the mass of one of the objects to 200 grams and keep the distance the same, the gravitational field strength would double. On the other hand, if you were to have them at the same mass, and double the distance between them, the gravitational field strength would be 1/4 of what it was to start with.