MAE 80 - Midterm 1 Practice Flashcards

Comprehensive vocabulary and concept flashcards covering kinematics, kinetics, orbital mechanics, and particle systems for MAE 80 Midterm 1.

Rotating Vector Derivative

A vector that rotates has a derivative with respect to time even if its length remains constant.

Time Derivative of a Rotating Unit Vector

Obtained by the cross product of the angular velocity vector and the unit vector itself.

Velocity (Constant Radius, Rotating)

v = d \times \frac{de_r}{dt} = d \times \text{e_r-dot}, where $d$ is a constant distance.

Velocity (Fixed Angle, Variable Radius)

$v = \text{d-dot} \times e_r$, where $e_r$ is fixed because the angle is not changing.

Radial Acceleration (Constant Radius)

In internal or circular motion with a constant radius, there is always a radial acceleration term present.

Centrifugal Acceleration

The -r(\text{\theta-dot})^2 term in the $e_r$ direction during circular motion.

Newton's Second Law ($F$)

Inside the formula $F = ma$, $F$ represents the sum of all external forces acting on the body.

Linear Momentum Conservation

Linear momentum in a specific direction is constant if the external forces in that direction are zero.

Centrifugal Force

An 'inertial' force representing motion; it is the opposite of centripetal force and not a real force like gravity or tension.

Normal Forces

Forces that the physical support provides to maintain the motion or position of an object.

Pendulum Tension (Cable)

Tension is maximum at the bottom ($6$ o'clock position) and can potentially reach zero at positions above $3$ and $9$ o'clock.

Friction

A force that always resists relative motion at the surface where it operates.

G-Force (Circular Path)

In high-speed flight, it is defined as the inertial force perpendicular to the plane's velocity.

Rated Speed

The speed that maintains a vehicle's position on a track even if there were no friction.

Track Speed (Below Rated Value)

The vehicle may slip or not depending on the friction level and how much lower the speed is than the rated value.

Angular Momentum (Particle)

The cross product of the position vector and the linear momentum ($\text{position vector} \times \text{linear momentum}$).

Orbit Transfer Maneuver (Rapid)

A maneuver where the distance of the object to the foci does not change during the rapid process.

Total System Acceleration

$M_{total} a_G = \text{Sum of all external forces only}$.

Center of Gravity (Internal Forces)

If only internal forces act (like a compressed spring breaking between two masses), the center of gravity continues to move at its original velocity ($v_o$).

Particle System Linear Momentum

Constant in a specific direction if the sum of external forces in that direction is zero.

Angular Momentum Derivative

$\frac{d}{dt} H_O = \text{Sum of moments of external forces}$, as internal force moments cancel each other out.

Total Mechanical Energy

The sum of kinetic and potential energy; it is conserved in systems where only conservative forces do work.

Impulsive Collision Dynamics

During the impact (e.g., bullet hitting a box), non-impulsive external forces like gravity and friction can often be ignored momentarily.

Internal Forces Net Work

Internal forces (like friction between two moving blocks) can do net work on a system and change its total kinetic energy.

Pulley Kinematic Constraint (Example)

A relationship between block velocities in a pulley system, such as $3V_B+V_A=0$, derived from constant cable length.