PHY 1020: Chapter 3 - Rotational Motion and Orbits

Vocabulary practice flashcards covering circular acceleration, rotational dynamics, satellite orbits, escape velocity, and black holes.

Centripetal Acceleration

Inward acceleration directed toward the center of a circular path that enables an object to move in a circle, given by the formula $a = \frac{v^2}{r}$.

Artificial Gravity

Simulated gravity in space that must be created through rotation, as correctly depicted in 2001 – A Space Odyssey.

Torque

The rotational force or tendency of a force to rotate an object about an axis, calculated as $\vec{\tau} = \vec{r} \times \vec{F}$.

Angular Momentum

The rotational analog of linear momentum that represents the tendency for objects to keep spinning, expressed as $\vec{L} = \vec{r} \times \vec{p} = I\vec{\omega}$.

Conservation of Angular Momentum

The physical principle stating $L_1 = L_2$, which expands to $M v_1 R_1 = M v_2 R_2$ and simplifies to $v_1 R_1 = v_2 R_2$.

Gravitational Constant ($G$)

The universal constant equal to $6.67 \times 10^{-11}\,\text{m}^3/(\text{kg}\cdot\text{s}^2)$.

Newton's Law of Universal Gravitation

The formula defining the attractive gravitational force between two masses $M$ and $m$ separated by distance $r$, written as $F_G = \frac{GMm}{r^2}$.

Orbital Velocity

The speed needed to maintain a stable orbit around a central body, derived by setting gravitational force equal to centripetal force: $v = \sqrt{\frac{GM}{r}}$.

International Space Station (ISS)

A space station located roughly $250\,\text{miles}$ above Earth that travels at approximately $17000\,\text{miles/hr}$ to complete an orbit every ~$90\,\text{minutes}$.

Low-Earth Orbit (LEO)

Any orbit where an object travels below $1200\,\text{miles}$ up, requiring higher speeds the closer the object is to Earth.

Global Positioning Satellites (GPS)

A satellite constellation orbiting around $12,000\,\text{miles}$ above Earth with an orbital period of about $12\,\text{hours}$ to accurately determine location.

Geosynchronous Satellites

Satellites located in High-Earth Orbit at about $30,000\,\text{miles}$ up that orbit at the same speed as Earth's rotation, remaining continuously overhead for TV and weather service.

Escape Velocity

The speed needed to break free from an object's gravitational attraction, calculated as $v_e = \sqrt{\frac{2GM}{r}}$, which equals $11\,\text{km/s}$ at Earth's surface.

Deimos

A moon with an escape velocity so low that taking a running jump on its surface would launch a person off like a slow rocket.

Black Hole

An object with an escape velocity from its center greater than the speed of light ($> 3 \times 10^8\,\text{m/s}$), preventing anything from escaping.

Event Horizon

Also known as the Schwarzschild Radius ($r = \frac{2GM}{v_e^2}$), the threshold around a black hole where escape velocity exceeds the speed of light.