Physics Lecture Notes: Momentum, Energy, and Motion

Flashcards covering physics concepts including momentum, energy, work, rotational motion, gravity, and Newton's laws based on lecture notes from Lectures 1-10.

Momentum

Inertia in motion; a property that quantifies the motion of an object.

Momentum Vector

A property indicating that momentum has both a magnitude and a direction.

Momentum (Symbol)

$$p$$

Momentum Units

$kg \cdot m/s$ or $Ns$

Momentum Equation

$$p = mv$$

Direct Proportionality in Momentum

Both mass and velocity are directly proportional to momentum.

Impulse

The change in momentum of an object or system of objects.

Impulse (Symbol)

$$\Delta p$$

Impulse Equation (Change)

$$\Delta p = p_{final} - p_{initial}$$

Impulse Equation (Force)

$$\Delta p = F \Delta t$$

Force and Impulse Relationship

Impulse is directly proportional to force.

Duration of Time and Impulse

Impulse is directly proportional to the duration of time over which force is applied.

Speeding Up Force Direction

Force needs to be applied in the same direction as the velocity.

Slowing Down Force Direction

Force needs to be applied in the opposite direction as the velocity.

Conservation of Momentum

The momentum of a system is conserved in the absence of external forces.

Momentum Conservation in Dimensions

In the absence of external forces, momentum is conserved in all dimensions (x, y, and z).

Kinetic Energy (Definition)

The energy that an object has by virtue of its motion.

Kinetic Energy (Symbol)

$$KE$$

Kinetic Energy (Units)

$J$ (Joules)

Kinetic Energy Equation

$$KE = \frac{1}{2} mv^2$$

Inelastic Collision

A collision where some of the kinetic energy ($KE$) of the system is converted into other forms of energy like heat or sound.

Elastic Collision

A collision where the kinetic energy ($KE$) of the system is conserved.

Perfectly Inelastic Collision

A collision where the maximum amount of $KE$ is lost and the two objects travel together after the collision.

Elastic Collision Characteristics

Occur when no heat is generated, no sound is made, and molecules do not physically deform.

Energy

The capability of an object to do useful work.

Work

The transfer of energy by applying a force to an object over a distance.

Work Equation

$$W = F_{\parallel} d$$

Joule (Definition)

The primary unit for energy and work; $1\,J = 1\,Nm$.

Newton (Symbol and Unit)

$$N = kg \cdot m/s^2$$

Potential Energy

Stored energy.

Kinetic Energy (Major Type)

Energy of motion.

Electric Potential Energy

Energy that comes from the arrangement of charged particles.

Chemical Energy

Energy that comes from the arrangement of atoms or molecules.

Nuclear Energy

Energy that comes from the nucleus of an atom.

Elastic Potential Energy

Energy that comes from the configuration of a deformable object.

Gravitational Potential Energy (Definition)

Energy that comes from the gravitational attraction between the Earth and an object of mass.

Gravitational Potential Energy (Symbol)

$$GPE$$

Gravitational Potential Energy Equation

$$GPE = mgh$$

Heat

Energy that flows between objects due to a temperature difference.

Friction Energy Conversion

Friction converts $KE$ to heat, which is frequently wasted energy.

Mechanical Energy (Definition)

Provides a way to describe the amount of $GPE$ and $KE$ of an object.

Mechanical Energy Equation

$$ME = GPE + KE$$

Conservation of Mechanical Energy

$ME$ is conserved in the absence of dissipative forces like friction or air drag.

Positive Work

Occurs when parallel force points in the same direction as the displacement, causing the object to speed up and gain $KE$.

Negative Work

Occurs when parallel force points in the opposite direction as the displacement, causing the object to slow down and lose $KE$.

Work-Energy Theorem

$W = \Delta KE$ or $W = KE_{final} - KE_{initial}$

Power (Definition)

The rate at which work is done.

Power (Symbol)

$$P$$

Power Units

$W$ (Watts) or $J/s$

Power Equation

$$P = \frac{W}{t}$$

Simple Machines

Devices that change direction or magnitude (or both) of an applied force.

Mechanical Advantage (Definition)

Multiplication of an input force by a simple machine.

Mechanical Advantage (Symbol)

$$MA$$

Mechanical Advantage Equation

$$MA = \frac{F_{out}}{F_{in}}$$

Translational Motion

Motion along a straight line.

Rotational Speed

The speed at which an object rotates about an axis.

Radian Measure Relation

$$2\pi = 1\text{ rotation}$$

Rotational Speed Units

$RPM$, $\text{degrees/s}$, or $rad/s$

Tangential Velocity (Definition)

Relates to rotational speed and distance from the center of rotation.

Tangential Velocity (Symbol)

$$V_t$$

Tangential Velocity Equation

$$V_t = 2\pi r / t$$

Tangential Velocity Direction

Tangent to the motion of the rotation.

Rotational Acceleration

Measures the change in rotational speed of an object.

Rotational Inertia

Measures how much an object resists changes to its rotational motion.

Torque (Definition)

A twist or a turn that causes an object to change its rotational motion.

Torque (Symbol)

$$\tau$$

Torque Units

$$Nm$$

Torque Equation

$$\tau = F_{\perp} r$$

Apparent Weight (Definition)

Comes from the support force acting on us.

Universal Gravitational Constant (G)

$$6.67 \times 10^{-11}\,N\cdot m^2/kg^2$$

Inverse-Square Law

Mathematical description of physical properties that decrease with the square of the distance ($\propto 1/d^2$).

Newton's Law of Universal Gravitation Equation

$$F = G \frac{m_1 m_2}{d^2}$$

Gravitational Acceleration (Little g)

The acceleration due to gravity on Earth's surface, equal to $-9.8\,m/s^2$.

Gravitational Fields

A model describing how objects interact due to gravity using arrows depicting mass movement.

General Relativity

Theory where motion is influenced by curves in "spacetime" caused by massive objects.

Projectile Motion

Description of the motion of an object that moves in free-fall, considering only gravity.

Ballistics

The study of objects that travel in projectile motion.

Projectile Path Shape

Parabola

Optimal Launch Angle for Horizontal Range

$$45^{\circ}$$

Satellite

A projectile that falls around Earth.

Orbit

Describes the path of a satellite around a planet or star; all are elliptical.

Circular Orbit

A special case where orbital height does not change and $KE + GPE = \text{constant}$.

Science

Systematic pursuit and organization of knowledge through questions, observations, and experiments.

Scientific Method

The process by which scientists come to answer questions about the universe.

Hypothesis

A proposed explanation based on observations that can be tested experimentally.

Theory

An explanation of how the universe works supported by multiple, repeated experiments.

Quantum Physics

Physical laws describing properties of matter and energy on a very small scale.

Newton's First Law

An object in motion tends to stay in motion; an object at rest tends to stay at rest, unless acted upon by an outside force.

Inertia

Describes the difficulty in changing an object's motion; caused by mass.

Mass

A physical property that relates to inertia.

Vector

A quantity that contains magnitude (strength) and direction.

Mechanical Equilibrium

A condition where the sum of all forces is zero and the object experiences no change in motion.

Displacement

A vector quantity representing the straight-line distance from one point to another.

Speed

The scalar rate at which an object changes its position.

Velocity

The vector rate at which an object changes its position.

Acceleration

The rate at which an object's velocity changes ($m/s^2$).

Newton's Second Law Equation

$$\sum F = ma$$

Static Friction

The force required to get an object at rest to start moving.

Kinetic Friction

The force between two objects where there is motion.

Terminal Speed

The speed at which air resistance equals gravity, resulting in dynamic equilibrium.