Isaac Newton compared the acceleration of the moon to the acceleration of objects on earth. Believing that gravitational forces were responsible for each, Newton was able to draw an important conclusion about the dependence of gravity upon distance. This comparison led him to conclude that the force of gravitational attraction between the Earth and other…
In the early 1600’s, German mathematician and astronomer Johannes Kepler mathematically analyzed known astronomical data in order to develop three laws to describe the motion of planets about the sun. Kepler’s three laws emerged from the analysis of data carefully collected over a span of several years by his Danish predecessor and teacher, Tycho Brahe. Kepler’s three laws of planetary…
Universal Gravitation Nearly every child knows of the word gravity. Gravity is the name associated with the mishaps of the milk spilled from the breakfast table to the kitchen floor and the youngster who topples to the pavement as the grand finale of the first bicycle ride. Gravity is the name associated with the reason for “what…
Circular motion is common to almost all sporting events. Whether it is sports car racing or track and field, baseball running or ice-skating, the motion of objects in circles is a common observation of sports viewers around the world. Like any object moving in a circle, the motion of these objects that we view from…
People are wild about amusement parks. Each day, we flock by the millions to the nearest park, paying a sizable hunk of money to wait in long lines for a short 60-second ride on our favourite roller coaster. The thought prompts one to consider what is it about a roller coaster ride that provides such…
Applications of Circular Motion Newton’s second law states that the acceleration of an object is directly proportional to the net force acting upon the object and inversely proportional to the mass of the object. The law is often expressed in the form of the following two equations. Newton’s Second Law and a Force Analysis Newton’s second…
There are three mathematical quantities that will be of primary interest to us as we analyze the motion of objects in circles. These three quantities are speed, acceleration and force. The speed of an object moving in a circle is given by the following equation. The acceleration of an object moving in a circle can be determined…
When the subject of circular motion is discussed, it is not uncommon to hear mention of the word centrifugal. Centrifugal, not to be confused with centripetal, means away from the center or outward. The use of or at least the familiarity with this word centrifugal, combined with the common sensation of an outward lean when experiencing circular motion, often creates…
An object moving in a circle is experiencing an acceleration. Even if moving around the perimeter of the circle with a constant speed, there is still a change in velocity and subsequently an acceleration. This acceleration is directed towards the center of the circle. And in accord with Newton’s second law of motion, an object which experiences an acceleration must…
An object moving in uniform circular motion is moving in a circle with a uniform or constant speed. The velocity vector is constant in magnitude but changing in direction. Because the speed is constant for such a motion, many students have the misconception that there is no acceleration. “After all,” they might say, “if I…