Mechanics 3 Semester 4 Examination Review

This set of vocabulary flashcards covers key concepts, formulas, and definitions from the Mechanics 3 Semester 4 exam, including rotational dynamics, energy, simple machines, and mechanical drives.

Torque ($T$)

A measure of the turning force applied to an object, calculated using the formula $T = F \times R$ and expressed in units of Newton-metres ($N \times m$).

Moment of Inertia ($I$)

A property of a body that determines the torque needed for a desired angular acceleration about a rotational axis, calculated as $I = m \times k^2$ with units of $kg \times m^2$.

Radius of Gyration ($k$)

The radial distance from the axis of rotation to a point where the total mass of the body could be concentrated without changing its moment of inertia.

Work ($WD$)

The product of the force applied to an object and the displacement caused by that force, calculated as $WD = F \times S$ in linear systems or $WD = T \times \theta$ in rotational systems, measured in Joules ($J$).

Power ($P$)

The rate at which work is done or energy is transferred, calculated as $P = T \times \theta$ or $P = F \times v$, with the standard unit being the Watt ($W$).

Kinetic Energy ($KE$)

The energy an object possesses due to its motion, calculated as $KE = \frac{1}{2}mv^2$ for linear motion or $KE = \frac{1}{2}I\times \theta^2$ for rotational motion, measured in Joules ($J$).

Law of the Machine

The mathematical relationship between the effort applied and the load lifted for a specific machine, typically expressed as a linear equation representing effort versus load.

Mechanical Advantage ($MA$)

The ratio of the actual load lifted by a machine to the actual effort applied to it, expressed by the formula $MA = \frac{\text{Actual Load}}{\text{Actual Effort}}$.

Velocity Ratio ($VR$)

The ratio of the distance moved by the effort to the distance moved by the load in a mechanical system, expressed as $VR = \frac{\text{Distance Moved by Effort}}{\text{Distance Moved by Load}}$.

Efficiency ($\nu$)

The ratio of mechanical advantage to velocity ratio, expressed as a percentage: $\nu = \frac{MA}{VR} \times 100$%.

Centripetal Acceleration ($a_{CENT}$)

The acceleration directed toward the center of a circular path, calculated as $a_{CENT} = \frac{v^2}{R} = \theta^2 \times r$.

Centripetal Force ($F$)

The force necessary to keep an object moving in a curved path, calculated as $F = \frac{m \times v^2}{r} = m \times \theta^2 \times r$.

Angle of Lap ($\theta$)

The angle of contact between a belt and a pulley, often measured in radians to calculate friction and power transmission in belt drives.

Fluid Coupling Clutch

A type of clutch that uses liquid to transmit rotational power between shafts, characterized by its smooth engagement and ability to handle varying loads.

Toothed Belts

Syncronous belt drives designed with teeth that mesh with a pulley, used for precise timing and preventing slippage in power transmission.