In physics, a slug is a unit of mass in the US customary system. Specifically, one slug is the amount of mass that will accelerate at a rate of 1 foot per second squared (1 ft/s²) when a force of 1 pound-force (lbf) is exerted on it.
To put it another way, it represents a mass equal to approximately 32.174 pounds (avoirdupois).
Key Characteristics of a Slug:
- Unit of Mass: It's a unit used to measure the amount of matter in an object.
- US Customary Units: Slugs are part of the foot-pound-second (FPS) or US customary system of units.
- Derived Unit: The slug is derived from force (pound-force), mass, and acceleration using Newton's second law of motion (F = ma).
Slug and Newton's Second Law
Newton's Second Law of Motion is F = ma, where:
- F is force
- m is mass
- a is acceleration
When force is measured in pounds-force (lbf) and acceleration in feet per second squared (ft/s²), mass is expressed in slugs. Therefore:
1 slug = 1 lbf / (1 ft/s²)
Relationship to Pounds (lbs)
A mass of 1 slug weighs approximately 32.174 lbf (or 143.117 Newtons) on Earth at standard gravity. This relationship stems from the acceleration due to gravity, which is about 32.174 ft/s². Essentially, one slug is the mass that, when subjected to Earth's gravity, experiences a force of approximately 32.174 pounds-force.
Difference Between Mass (Slug) and Weight (Pound-force)
It's crucial to differentiate between mass and weight. Mass is the amount of matter in an object and remains constant regardless of location. Weight, on the other hand, is the force of gravity acting on that mass and can vary depending on the gravitational field. Slugs measure mass, while pounds-force measure weight (force).
Why Use Slugs?
Slugs provide a consistent unit of mass within the US customary system, ensuring calculations based on Newton's Laws are accurate when force is in pounds-force and acceleration is in feet per second squared. Without the slug, you'd have to convert pounds (which are commonly used as a unit of weight) to a mass unit like kilograms and then convert forces from pounds-force to Newtons, which is less convenient in systems where pounds-force are already used.
