Glossary
Acceleration
The rate at which an object's velocity changes over time, involving changes in speed, direction, or both. It is a vector quantity, measured in meters per second squared (m/s²).
Example:
A car speeding up from a stop sign experiences positive acceleration as its velocity increases.
Acceleration of the system's center of mass
The rate at which the velocity of a system's center of mass changes over time, determined by the net external force acting on the system and its total mass.
Example:
If two connected blocks are pulled across a surface, their combined acceleration of the system's center of mass will be the same, even if individual parts move differently relative to each other.
Balanced forces
Forces acting on an object that are equal in magnitude and opposite in direction, resulting in a net force of zero. An object under balanced forces maintains a constant velocity or remains at rest.
Example:
A book resting on a table experiences balanced forces from gravity pulling it down and the normal force pushing it up, keeping it stationary.
Coefficient of kinetic friction
A dimensionless scalar value that describes the ratio of the force of kinetic friction to the normal force between two surfaces in relative motion.
Example:
A higher coefficient of kinetic friction between tires and the road means better grip and more resistance to skidding.
Directly proportional
A relationship where two quantities increase or decrease together at a constant ratio; in Newton's Second Law, acceleration is directly proportional to net force.
Example:
If you double the force applied to a cart, its acceleration will also double, showing a directly proportional relationship.
External forces
Forces that originate from outside the defined system and act upon it. These forces are capable of changing the system's total momentum or causing its center of mass to accelerate.
Example:
When a car brakes, the friction between the tires and the road is an external force that slows the car down.
Force
A push or a pull that can cause an object to accelerate or change its state of motion. It is a vector quantity, possessing both magnitude and direction.
Example:
The force of gravity pulls an apple towards the Earth, causing it to fall.
Free-Body Diagram
A visual representation of all external forces acting on a single object or system, drawn as vectors originating from the object's center.
Example:
To solve a problem involving a block on an inclined plane, drawing a free-body diagram helps identify gravitational, normal, and frictional forces.
Free-body diagrams
A visual representation used to analyze forces, showing all external forces acting on a single isolated object. Arrows represent forces, indicating their magnitude and direction.
Example:
Drawing a free-body diagram for a pendulum helps visualize the tension in the string and the gravitational force acting on the bob.
Frictional force
A force that opposes relative motion or tendency of motion between two surfaces in contact, arising from microscopic irregularities.
Example:
When a book slides across a table, the frictional force acts opposite to its direction of motion, eventually bringing it to a stop.
Internal Forces
Forces that act between objects within a defined system, which do not affect the motion of the system's center of mass.
Example:
When a person pushes against the inside of a car, these are internal forces that do not cause the car to accelerate.
Internal forces
Forces that act between objects or parts within a defined system. These forces do not change the motion of the system's center of mass.
Example:
The tension in a rope connecting two blocks is an internal force if both blocks are considered part of the same system.
Inversely proportional
A relationship where one quantity increases as the other decreases, and vice versa; in Newton's Second Law, acceleration is inversely proportional to mass.
Example:
Applying the same force to a heavier object will result in less acceleration, illustrating an inversely proportional relationship between mass and acceleration.
Kinematics
The branch of mechanics that describes the motion of points, objects, and groups of objects without considering the causes of motion (forces). It focuses on displacement, velocity, and acceleration.
Example:
Calculating how far a projectile travels horizontally, given its initial velocity and launch angle, is a problem in kinematics.
Kinematics
The branch of mechanics that describes the motion of points, objects, and groups of objects without considering the causes of motion.
Example:
Calculating the final velocity of a ball after it has fallen for a certain time, without considering air resistance, is a problem in kinematics.
Mass
A measure of an object's inertia, representing the amount of matter it contains and its resistance to acceleration. It is a scalar quantity, measured in kilograms (kg).
Example:
A bowling ball has a much larger mass than a tennis ball, which is why it requires a greater force to achieve the same acceleration.
Net External Force
The vector sum of all forces exerted on a system by objects outside the system, which is solely responsible for changing the system's center of mass velocity.
Example:
For a car moving, the engine's thrust and air resistance are net external forces, while the forces between the engine parts are internal.
Net force
The vector sum of all individual forces acting on an object. It is the total force that determines the object's acceleration according to Newton's Second Law.
Example:
In a tug-of-war, if one team pulls with 500 N and the other with 400 N, the net force on the rope is 100 N towards the stronger team.
Net force
The vector sum of all individual forces acting on an object or system, determining its acceleration.
Example:
If you push a box with 10 N to the right and a friend pushes with 5 N to the left, the net force on the box is 5 N to the right.
Newton's Second Law
States that an object's acceleration is directly proportional to the net force acting on it and inversely proportional to its mass ($\vec{F} = m\vec{a}$). It quantifies how forces cause changes in an object's motion.
Example:
When a soccer player kicks a ball, Newton's Second Law describes how the force of the kick causes the ball to accelerate across the field.
Newton's Second Law
A fundamental principle stating that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Example:
When a rocket engine ignites, the large net force it produces causes a significant acceleration of the rocket, demonstrating Newton's Second Law.
Normal force
The component of a contact force perpendicular to the surface that an object rests on or is in contact with, preventing it from passing through the surface.
Example:
When a book rests on a table, the table exerts an upward normal force on the book, balancing the book's weight.
Total mass of the system
The sum of the masses of all individual components within a defined system, which resists changes in the system's motion.
Example:
When analyzing a car towing a trailer, the total mass of the system includes both the car's mass and the trailer's mass.
Unbalanced Forces
Forces acting on an object that do not cancel each other out, resulting in a non-zero net force and causing the object to accelerate.
Example:
A car speeding up from a stop experiences unbalanced forces because the forward thrust from the engine is greater than the opposing forces like air resistance and friction.
Unbalanced forces
Forces acting on an object that do not cancel each other out, resulting in a non-zero net force. These forces cause an object to accelerate in the direction of the net force.
Example:
If you push a box with 10 N of force to the right and your friend pushes with 5 N to the left, the unbalanced forces will cause the box to accelerate to the right.