Glossary
Banked Curves
Roads or tracks that are angled to allow vehicles to navigate turns at higher speeds by using the normal force component to provide centripetal force.
Example:
Race cars on a banked curve can maintain high speeds without relying solely on friction, as the incline helps push them towards the center of the turn.
Centripetal Acceleration
Acceleration directed towards the center of a circular path, responsible for changing an object's direction of velocity while maintaining constant speed.
Example:
When a car takes a sharp turn, the friction between the tires and the road provides the centripetal acceleration that keeps the car from skidding off the curve.
Conical Pendulums
A pendulum that swings in a horizontal circle, where the tension in the string provides both the vertical force to balance gravity and the horizontal centripetal force.
Example:
An amusement park swing ride operates like a conical pendulum, with riders moving in a circle as the chains angle outwards.
Forces in Circular Motion
The net force acting on an object moving in a circular path, which is always directed towards the center of the circle and causes centripetal acceleration.
Example:
When swinging a ball on a string in a horizontal circle, the tension in the string provides the necessary forces in circular motion.
Frequency (f)
The number of revolutions or cycles an object completes per unit of time.
Example:
If a blender blade spins 300 times in one second, its frequency is 300 Hertz.
Kepler's Third Law
A law stating that the square of a planet's orbital period is directly proportional to the cube of its average orbital radius, relating the motion of orbiting bodies to the mass of the central body.
Example:
Kepler's Third Law explains why planets farther from the Sun have significantly longer orbital periods than those closer to it.
Mass of Central Body
The mass of the larger object around which another body is orbiting, which is a key factor determining the orbital characteristics of the smaller body.
Example:
In the case of Earth orbiting the Sun, the Sun is the mass of central body that dictates Earth's orbital speed and period.
Net Acceleration in Circles
The vector sum of centripetal acceleration (changing direction) and tangential acceleration (changing speed), pointing at an angle to the circular path when both are present.
Example:
When a spinning top slows down, its net acceleration in circles is not purely radial but has a component that opposes its tangential motion.
Orbital Period
The time it takes for a celestial body or satellite to complete one full orbit around another body.
Example:
The orbital period of the Moon around Earth is approximately 27.3 days.
Orbital Radius
The average distance of an orbiting body from the center of the body it orbits.
Example:
The orbital radius of Earth around the Sun is approximately 150 million kilometers.
Period (T)
The time it takes for an object to complete one full revolution or cycle in its circular path.
Example:
The period of a Ferris wheel is the time it takes for one cabin to make a complete rotation.
Radius of Circular Path
The distance from the center of the circular path to the object moving along the path.
Example:
For a child on a merry-go-round, the radius of circular path is the distance from the center pole to the child's position.
Tangential Acceleration
Acceleration that acts along the direction of motion (tangent to the circular path), causing a change in the object's speed.
Example:
If a car speeds up while going around a curve, it has both centripetal acceleration and tangential acceleration.
Tangential Speed
The magnitude of the velocity vector of an object moving in a circular path, representing how fast the object is moving along the circumference.
Example:
A satellite orbiting Earth at a constant tangential speed means it covers equal distances along its orbit in equal time intervals.
Uniform Circular Motion
Motion of an object in a circular path at a constant tangential speed, meaning only its direction of velocity is changing due to centripetal acceleration.
Example:
A satellite orbiting Earth in a perfectly circular path at a steady speed is an example of uniform circular motion.
Universal Gravitational Constant (G)
A fundamental physical constant that quantifies the strength of the gravitational force between any two objects with mass.
Example:
The Universal Gravitational Constant (G) is used in Newton's Law of Universal Gravitation to calculate the attractive force between any two masses.
Vertical Loops
A scenario where an object moves in a circular path in a vertical plane, often involving gravity and tension or normal force.
Example:
On a roller coaster, riders experience varying normal forces as the car navigates a vertical loop, feeling heaviest at the bottom and lightest at the top.