Glossary
Angular Velocity (ω)
The rate at which an object rotates or revolves around a center point, measured in radians per second. It describes how fast the angle changes.
Example:
A spinning record player has a constant Angular Velocity, indicating how many radians it turns per second.
Banked Curves
Roads or tracks that are tilted at an angle to the horizontal, designed to allow vehicles to navigate turns at higher speeds by using a component of the normal force to provide centripetal force.
Example:
Race tracks often feature Banked Curves to enable cars to maintain high speeds without skidding off.
Banked Surfaces
Inclined surfaces, like racetrack turns, designed to use components of the normal force and static friction to provide the necessary centripetal force for vehicles.
Example:
Race cars on a banked surface can take turns at higher speeds because the banking helps provide the inward force, reducing reliance on friction.
Centripetal Acceleration
The acceleration that keeps an object moving in a circle, always directed towards the center of the circle, constantly changing the direction of the velocity.
Example:
When a car takes a sharp turn, the friction between the tires and the road provides the centripetal acceleration needed to keep the car on its curved path.
Centripetal Acceleration (a_c)
The acceleration experienced by an object in circular motion, always directed towards the center of the circle. It is responsible for changing the direction of the object's velocity.
Example:
When a car rounds a curve, the friction between the tires and the road provides the Centripetal Acceleration needed to keep the car on the curved path.
Centripetal Force
The net force acting on an object moving in a circular path, always directed towards the center of the circle, responsible for causing centripetal acceleration.
Example:
For a satellite orbiting Earth, gravity acts as the centripetal force, pulling the satellite towards the planet's center.
Centripetal Force (F_c)
The net force that causes centripetal acceleration, always directed towards the center of the circular path. It is not a new type of force but rather the net force acting radially inward.
Example:
The tension in a string when swinging a ball in a horizontal circle acts as the Centripetal Force.
Conical Pendulum
A pendulum that swings in a horizontal circle, where the tension in the string provides the centripetal force through its horizontal component.
Example:
A tetherball swinging around a pole is an example of a conical pendulum, with the rope's tension keeping it in a circular path.
Critical Speed
The minimum speed an object must have at the top of a vertical loop to maintain contact with the track or string. At this speed, the normal force or tension becomes zero.
Example:
For a roller coaster to successfully complete a loop, it must maintain at least the Critical Speed at the very top.
Free Body Diagrams (FBDs)
A visual representation used to analyze forces acting on an object, showing all forces as vectors originating from the object's center of mass.
Example:
Drawing a Free Body Diagram for a car on a banked curve helps identify the components of the normal force and friction.
Frequency (f)
The number of complete revolutions or cycles an object makes per unit of time in circular motion.
Example:
If a fan blade completes 10 rotations per second, its frequency is 10 Hz.
Ideal Banked Curve
A banked curve designed for a specific speed where the horizontal component of the normal force alone provides the necessary centripetal force, requiring no friction.
Example:
On an Ideal Banked Curve, a car traveling at the design speed would not need any friction to stay on the road.
Kinetic Friction
A force that opposes the relative motion between two surfaces in contact when they are sliding past each other. In circular motion, it can contribute to or oppose the centripetal force.
Example:
When a car skids on a banked curve, the Kinetic Friction between the tires and the road acts to slow it down or prevent further sliding.
Net Acceleration
The vector sum of an object's centripetal and tangential accelerations, representing the total rate of change of its velocity.
Example:
If a car is speeding up while turning, its net acceleration will be a vector pointing somewhere between the direction of motion and the center of the turn.
Non-Uniform Circular Motion
Circular motion where the object's speed is not constant, meaning there is both a centripetal acceleration and a tangential acceleration.
Example:
A roller coaster going through a loop where its speed changes as it moves up and down is an example of Non-Uniform Circular Motion.
Period (T)
The time it takes for an object to complete one full revolution or cycle in circular motion.
Example:
The period of Earth's orbit around the Sun is approximately 365 days.
Period (T)
The time it takes for an object to complete one full revolution or cycle in circular motion. It is inversely related to frequency.
Example:
The Period of Earth's orbit around the Sun is approximately 365 days.
Tangential Acceleration
The component of acceleration that acts along the direction of motion, tangent to the circular path, and changes the object's speed.
Example:
When a car speeds up while turning, it experiences tangential acceleration in addition to centripetal acceleration.
Tangential Acceleration (a_t)
The component of acceleration that is parallel to the tangential velocity, causing a change in the object's speed along the circular path.
Example:
When a car speeds up while going around a curve, it experiences Tangential Acceleration in addition to centripetal acceleration.
Tangential Velocity (v)
The instantaneous linear speed of an object along the circular path, always directed tangent to the circle at any given point.
Example:
If a string holding a ball in circular motion breaks, the ball will fly off in the direction of its Tangential Velocity at that instant.
Total Acceleration
The vector sum of the centripetal acceleration and the tangential acceleration in non-uniform circular motion. It represents the overall acceleration of the object.
Example:
In a car accelerating around a bend, the Total Acceleration vector points somewhere between the center of the curve and the direction of motion.
Uniform Circular Motion
Motion of an object in a circular path at a constant speed, meaning only the direction of its velocity changes.
Example:
A satellite orbiting Earth at a constant altitude and speed is undergoing uniform circular motion.
Uniform Circular Motion (UCM)
The motion of an object moving in a circular path at a constant speed. Although the speed is constant, the velocity is continuously changing due to the changing direction.
Example:
A satellite orbiting Earth at a steady altitude and speed is undergoing Uniform Circular Motion.
Vertical Circles
Circular motion occurring in a vertical plane, where gravity significantly influences the object's speed and the forces acting on it at different points.
Example:
Swinging a bucket of water over your head in a loop demonstrates motion in Vertical Circles.
Vertical Loops
A specific scenario in circular motion where an object moves in a vertical circle, often involving gravity and normal force or tension.
Example:
A rollercoaster car going through a vertical loop requires a minimum speed at the top to prevent it from falling off the track.