Linear Momentum Formula Calculator

\[ p = m v \]

1. What is the Linear Momentum Formula Calculator?

Definition: This calculator computes the linear momentum (\(p\)) of an object, defined as the product of its mass (\(m\)) and velocity (\(v\)) using the formula \(p = m v\).

Purpose: It is used in physics to quantify the momentum of moving objects, applicable in collision analysis, mechanics, and motion studies.

2. How Does the Calculator Work?

The calculator uses the linear momentum formula:

Formula: \[ p = m v \] where:

\(p\): Linear momentum (kg·m/s, lb·ft/s)
\(m\): Mass (kg, g, lb)
\(v\): Velocity (m/s, km/s, ft/s, mph)

Unit Conversions:

Mass:
- 1 kg = 1 kg
- 1 g = 0.001 kg
- 1 lb = 0.45359237 kg
Velocity:
- 1 m/s = 1 m/s
- 1 km/s = 1000 m/s
- 1 ft/s = 0.3048 m/s
- 1 mph = 0.44704 m/s
Linear Momentum (Output):
- 1 kg·m/s = 1 kg·m/s
- 1 lb·ft/s = \( \frac{1}{0.45359237 \times 0.3048} \) kg·m/s \(\approx 7.23301385 \, \text{kg·m/s}\)

The linear momentum is calculated in kg·m/s and can be converted to the selected output unit (kg·m/s, lb·ft/s).

Steps:

Enter the mass (\(m\)) and velocity (\(v\)) with their units (default: \(m = 2 \, \text{kg}\), \(v = 5 \, \text{m/s}\)).
Convert inputs to SI units (kg, m/s).
Validate that mass is greater than 0.
Calculate the linear momentum in kg·m/s using the formula.
Convert the linear momentum to the selected output unit.
Display the result, rounded to 4 decimal places.

3. Importance of Linear Momentum Calculation

Calculating linear momentum is crucial for:

Physics: Analyzing the motion of objects in collisions, explosions, and other interactions where momentum is conserved.
Engineering: Designing vehicles, safety systems, and machinery that account for momentum in dynamic scenarios.
Education: Teaching the principles of momentum and Newton’s laws in classical mechanics.

4. Using the Calculator

Examples:

Example 1: Calculate the linear momentum for \(m = 2 \, \text{kg}\), \(v = 5 \, \text{m/s}\), output in kg·m/s:
- Enter \(m = 2 \, \text{kg}\), \(v = 5 \, \text{m/s}\).
- Linear momentum: \(p = 2 \times 5 = 10 \, \text{kg·m/s}\).
- Output unit: kg·m/s (no conversion needed).
- Result: \( \text{Linear Momentum} = 10.0000 \, \text{kg·m/s} \).
Example 2: Calculate the linear momentum for \(m = 4.40925 \, \text{lb}\), \(v = 10 \, \text{mph}\), output in lb·ft/s:
- Enter \(m = 4.40925 \, \text{lb}\), \(v = 10 \, \text{mph}\).
- Convert: \(m = 4.40925 \times 0.45359237 = 2 \, \text{kg}\), \(v = 10 \times 0.44704 = 4.4704 \, \text{m/s}\).
- Linear momentum in kg·m/s: \(p = 2 \times 4.4704 = 8.9408 \, \text{kg·m/s}\).
- Convert to output unit (lb·ft/s): \(8.9408 \times \frac{1}{0.45359237 \times 0.3048} \approx 64.6685 \, \text{lb·ft/s}\).
- Result: \( \text{Linear Momentum} = 64.6685 \, \text{lb·ft/s} \).

5. Frequently Asked Questions (FAQ)

Q: What is linear momentum?
A: Linear momentum is a measure of an object’s motion, defined as the product of its mass and velocity, and is a vector quantity conserved in isolated systems.

Q: Why must mass be greater than zero?
A: Zero or negative mass is physically meaningless in this context, as momentum requires a massive object.

Q: Can linear momentum be negative?
A: Yes, linear momentum can be negative if the velocity is negative, indicating motion in the opposite direction.