Glossary
Area under a force-time graph
The graphical representation of the total impulse delivered by a force over a specific time interval. It is equivalent to the integral of force with respect to time.
Example:
Analyzing the area under a force-time graph for a car crash helps engineers determine the total 'push' on the vehicle during impact.
Change in momentum
The difference between an object's final momentum and its initial momentum, indicating how much the object's motion has been altered. It is a vector quantity.
Example:
When a baseball player catches a fast-moving ball, the change in momentum of the ball is significant, requiring the player to apply a force to stop it.
Change in momentum
The difference between an object's final momentum and its initial momentum. It is a vector quantity and is equal to the impulse applied to the object.
Example:
When a baseball is caught, its change in momentum is significant, going from a high velocity to zero.
Force-time graph area
The area enclosed by a force-time graph and the time axis represents the total impulse delivered to an object during that time interval.
Example:
If you plot the varying force of a golf club hitting a ball against time, the force-time graph area under the curve will tell you the impulse imparted to the ball.
Impulse
A measure of the change in momentum of an object, calculated as the average force applied over a specific time interval. It is a vector quantity.
Example:
A car's airbag increases the time over which the force of impact acts on a passenger, reducing the impulse felt by the passenger and minimizing injury.
Impulse
A vector quantity representing the effect of a force acting over a time interval, causing a change in an object's momentum. It is calculated as the integral of net force over time.
Example:
A tennis racket hitting a ball delivers a significant impulse to change the ball's direction and speed.
Impulse vector
The vector quantity representing impulse, which has both magnitude and direction. Its direction is always the same as the net force applied.
Example:
If you push a box to the right, the impulse vector will also point to the right, indicating the direction of momentum change.
Impulse-Momentum Theorem
A fundamental principle stating that the impulse applied to an object is equal to the change in its momentum. This theorem directly links force, time, and motion.
Example:
According to the Impulse-Momentum Theorem, the impulse from a tennis racket hitting a ball directly equals the change in the ball's momentum, determining its new speed and direction.
Impulse-Momentum Theorem
A fundamental principle stating that the impulse applied to an object is equal to the change in its momentum. This theorem links force, time, and motion.
Example:
The Impulse-Momentum Theorem explains why airbags reduce injury: they increase the time over which the force acts, thus reducing the magnitude of the force for the same change in momentum.
Momentum-time graph slope
The slope of a momentum-time graph at any given point represents the net external force acting on the object at that instant.
Example:
If a rocket's momentum-time graph slope is constant and positive, it indicates a constant net thrust force propelling it forward.
Net external force
The vector sum of all external forces acting on an object or system. It dictates how quickly an object's momentum changes.
Example:
When a soccer ball is kicked, the net external force from the player's foot causes the ball to accelerate and change its momentum.
Net external force
The vector sum of all forces acting on a system from outside the system. It is directly proportional to the rate of change of the system's momentum.
Example:
When a car accelerates, the engine's thrust minus air resistance and friction constitutes the net external force causing its momentum to change.
Newton's Second Law
States that the net force acting on an object is equal to the rate at which its momentum changes, or more commonly, mass times acceleration ($F_{net} = ma$). It is a special case of the impulse-momentum theorem when mass is constant.
Example:
When a constant force is applied to a shopping cart, Newton's Second Law explains why the cart accelerates at a rate inversely proportional to its mass.
Newton's second law (momentum form)
States that the net external force acting on an object is equal to the rate of change of its momentum with respect to time. This is the more general form of F=ma.
Example:
For a rocket, Newton's second law in its momentum form () is crucial because the rocket's mass changes as it expels fuel.
Rate of mass change
The derivative of mass with respect to time, indicating how quickly the mass of a system is increasing or decreasing. It is relevant when applying Newton's second law to systems with variable mass.
Example:
The thrust of a rocket is directly related to the rate of mass change (fuel expulsion) multiplied by the exhaust velocity.
Slope of a momentum-time graph
The graphical representation of the net external force acting on an object at any given moment. A steeper slope indicates a larger force.
Example:
If the slope of a momentum-time graph is constant and positive, it means a constant net force is acting in the positive direction.
Units of Impulse/Momentum
The standard units for both impulse and momentum, which are dimensionally equivalent. Impulse is measured in Newton-seconds (N⋅s), and momentum in kilogram-meters per second (kg⋅m/s).
Example:
If a problem asks for the impulse delivered, the answer should be expressed in N⋅s, which is equivalent to kg⋅m/s if you were calculating a change in momentum.
Vector
A physical quantity that has both magnitude (size) and direction. Both impulse and momentum are vector quantities, meaning their direction is crucial in calculations.
Example:
When analyzing a collision, it's essential to treat velocity, momentum, and impulse as vectors to correctly account for changes in direction, such as a ball bouncing off a wall.