Module 3: Motion in Two Dimensions
As you have learned, horizontal and vertical motion can and must be analyzed independently when dealing with projectiles. Each component of the motion is determined by the initial conditions in that direction, horizontal or vertical. In the horizontal direction, there is no acceleration, while in the vertical direction, object accelerate with the gravitational acceleration of 9.8 meters per second squared. Kinematics equations work effectively in analyzing the horizontal and vertical motion of a projectile. This analysis is greatly simplified due to the fact that velocity is constant in the horizontal direction.
When objects are launched horizontally, the initial vertical velocity is zero, and these situations are more simple to analyze than projectiles launched at an angle. With different launch angles, you must employ simple trigonometry to separate the initial horizontal and vertical components of the velocity in your analysis.
Circular motion occurs due to a center-directed net force. This net force is made up of real forces and is called a centripetal force. The magnitude of the centripetal force is mv2/r and this force accelerates objects towards the center of a circular path with an acceleration of v2/r without changing their speed. Objects moving in vertical circles momentarily obey these rules when they are at the top and the bottom of their paths, where the forces are acting vertically and can easily be resolved into a centripetal force.
Newton’s Law of Universal Gravitation states that every mass in the universe is attracted to every other mass by a force that is directly proportional to the product of the masses and inversely proportional to the distance between them. This is known as an inverse square law, of which there are several in physics. Universal gravitation allows us to understand satellite and planetary motion as the gravitational force provides a centripetal force which keeps planets and satellites moving in nearly circular orbits.
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