Physics: Machines, Energy, and Rotational Motion

Vocabulary flashcards covering the principles of simple machines, mechanical efficiency, rotational motion, torque, center of gravity, and rotational inertia.

Principle of a Machine

A concept based on the conservation of energy stating that work input equals work output, expressed as $(\text{Force} \times \text{distance})_{\text{input}} = (\text{force} \times \text{distance})_{\text{output}}$.

Simple Machine

A mechanical device that multiplies the effect of an applied force, where a small force applied over a large distance produces a large force applied over a small distance. The six basic types are the inclined plane, screw, wedge, wheel and axle, lever, and pulley.

Fulcrum

The fixed point of support on which a lever rotates.

Pulley

A simple machine that operates like a lever with equal arms to change the direction of an input force, or when combined in multiple strands, allows a load to be lifted with a fraction of the input force.

Efficiency

The percentage of work put into a machine that is converted into useful work output, defined mathematically as $\text{Efficiency} = \frac{\text{useful energy output}}{\text{total energy input}}$.

Recycled Energy

The re-employment of energy that would otherwise be wasted, such as capturing and using heat from a power plant to warm buildings.

Circular Motion

The motion that occurs when an object turns about an internal axis (also called rotation), characterized by tangential speed and rotational speed.

Tangential Speed ($v$)

The linear distance traveled by a point on a rotating object divided by the time taken to travel that distance ($v = r\omega$), which is higher for points farther from the center of rotation.

Rotational Speed ($\omega$)

The number of rotations or revolutions per unit of time (also known as angular speed), which is identical for all parts of a rigid rotating body.

Torque

The tendency of a force to cause rotation, calculated as $\text{Torque} = \text{lever arm} \times \text{force}$, where only the perpendicular component of the applied force contributes to rotational movement.

Lever Arm

The perpendicular distance from the axis of rotation or pivot point to the line along which the applied force acts.

Center of Mass

The average position of all the mass that makes up an object.

Center of Gravity (CG)

The average position of weight distribution, or the imaginary point where the total weight of a material body may be considered to be concentrated.

Stable Equilibrium

A condition in which a vertical line drawn straight downward from an object's center of gravity falls inside the base of support, allowing the object to remain balanced.

Rotational Inertia ($I$)

The property of an object to resist changes in its rotational state of motion (also called moment of inertia), which depends on the mass of the object and the distribution of that mass relative to the axis of rotation.

Rotational Inertia Formulas of Common Geometries

Formulas describing resistance to rotation based on shape and axis: simple pendulum ($I = mr^2$), hoop about normal axis ($I = mr^2$), hoop about diameter ($I = \frac{1}{2}mr^2$), stick about end ($I = \frac{1}{3}mL^2$), stick about CG ($I = \frac{1}{12}mL^2$), solid cylinder ($I = \frac{1}{2}mr^2$), and solid sphere about CG ($I = \frac{2}{5}mr^2$).