What are the three laws of motion?

The First Law (Law of Inertia) states that objects at rest stay at rest, and objects in motion stay in motion at constant velocity, unless acted upon by a net force. The Second Law (F = ma) relates force, mass, and acceleration. The Third Law states that for every action, there is an equal and opposite reaction.

How do I find force using the Second Law?

Select "Newton's Second Law" and provide any two of the three values (force, mass, acceleration). The tool will solve for the third. For example, if you know mass (10 kg) and acceleration (5 m/s²), enter those values and leave force empty. The result will be F = ma = 10 × 5 = 50 N.

What is the difference between kinetic and potential energy?

Kinetic energy (KE = ½mv²) is the energy of motion and depends on mass and velocity. Potential energy (PE = mgh) is stored energy due to position and depends on mass, gravitational acceleration, and height. An object can have both types of energy simultaneously.

How does universal gravitation work?

The Law of Universal Gravitation (F = G(m₁m₂)/r²) determines the gravitational force between any two masses. G is the gravitational constant (6.674 × 10⁻¹¹ m³/kg/s²). The force is always attractive and depends on both masses and the distance between them.

What is momentum and why is it important?

Momentum (p = mv) is the product of mass and velocity. It's a conserved quantity, meaning total momentum before and after a collision remains constant (assuming no external forces). This makes momentum essential for analyzing collisions and interactions.

How do I find work when force is at an angle?

Use the Work equation (W = Fdcos(θ)) and include the angle between the force and displacement vectors. When the force is parallel to motion (θ = 0°), work is maximum. When perpendicular (θ = 90°), no work is done.

Classical Mechanics Calculator - Physics, Forces & Motion Solver

Solve physics problems for force, motion, and energy. Free classical mechanics calculator using Newton's laws for students and engineering professionals.

Select Formula

Newton's First Law

Law of Inertia

Newton's Second Law

F = ma

Newton's Third Law

Action and Reaction

Universal Gravitation

F = G(m₁m₂)/r²

Momentum

p = mv

Kinetic Energy

KE = ½mv²

Potential Energy

PE = mgh

Work

W = Fdcos(θ)

Power

P = W/t

Impulse

J = Ft

Centripetal Force

F_c = mv²/r

Newton's Second Law

F = ma

2 inputs needed

Quick Examples

Car Acceleration

Bicycle Push

Rocket Thrust

Football Kick

Input Values

Force

Mass

Acceleration

m/s²

Important Disclaimer

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Solve physics problems involving forces, motion, gravitation, energy, and momentum. Ideal for students, educators, and professionals working with classical mechanics. Get instant results with detailed step-by-step solutions for 11 essential physics formulas.

How to Use Classical Mechanics Calculator

Choose Your Formula

Select from 11 physics equations using the dropdown menu. Options include the three laws of motion, universal gravitation, energy equations, momentum, work, power, impulse, and centripetal force.

Enter Your Values

Input the known quantities for your selected equation. Most equations allow you to solve for one unknown when you provide the others. For instance, with F = ma, you can find force from mass and acceleration, or determine acceleration from force and mass.

View Results

Click "Calculate" to see your results. The tool displays all computed values with proper units and includes a detailed step-by-step solution showing how each result was obtained.

Calculator Features

⚛️

Three Laws of Motion

Solve problems involving forces, acceleration, and motion using all three fundamental laws

🌍

Universal Gravitation

Find gravitational forces between any two masses using the law of universal gravitation

⚡

Energy Equations

Work with kinetic energy, potential energy, work, and power with detailed solutions

🎯

Momentum & Impulse

Solve problems involving linear momentum, impulse, and related quantities

🔄

Centripetal Force

Determine the force required for circular motion

📊

Step-by-Step Solutions

See detailed work showing how each result is obtained

✅

Input Validation

Automatic checks ensure you provide the correct number of inputs for each equation

Complete Function List

First Law of Motion (Law of Inertia) - Analyze equilibrium conditions:
Second Law of Motion (F = ma) - Find force, mass, or acceleration:
Third Law of Motion - Determine action and reaction forces:
Universal Gravitation - Find gravitational force between masses:
Momentum (p = mv) - Solve for momentum, mass, or velocity:
Kinetic Energy (KE = ½mv²) - Find kinetic energy, mass, or velocity:
Potential Energy (PE = mgh) - Determine gravitational potential energy:
Work (W = Fdcos(θ)) - Find work done by a force:
Power (P = W/t) - Solve for power, work, or time:
Impulse (J = Ft) - Find impulse, force, or time:
Centripetal Force (F_c = mv²/r) - Determine force for circular motion:

Common Calculations & Examples

Example 1: Calculate Force from Mass and Acceleration

Problem: A 10 kg object accelerates at 5 m/s². What force is applied?

Steps:

Select "Newton's Second Law" from the formula dropdown
Enter mass: 10 kg
Enter acceleration: 5 m/s²
Leave force empty (this is what we're calculating)
Click "Calculate"

Result: Force = 50 N

Explanation: Using F = ma, we get F = 10 kg × 5 m/s² = 50 N. This demonstrates the relationship between force, mass, and acceleration.

Example 2: Calculate Kinetic Energy

Problem: A 2 kg ball moves at 10 m/s. What is its kinetic energy?

Steps:

Select "Kinetic Energy" from the formula dropdown
Enter mass: 2 kg
Enter velocity: 10 m/s
Leave kinetic energy empty
Click "Calculate"

Result: Kinetic Energy = 100 J

Explanation: Using KE = ½mv², we get KE = 0.5 × 2 kg × (10 m/s)² = 100 J. Energy of motion depends on both mass and the square of velocity.

Example 3: Calculate Gravitational Force

Problem: Find the gravitational force between Earth (5.97 × 10²⁴ kg) and a 70 kg person at Earth's surface (6.37 × 10⁶ m from center).

Steps:

Select "Universal Gravitation" from the formula dropdown
Enter mass1: 5.97e24 kg
Enter mass2: 70 kg
Enter distance: 6.37e6 m
Click "Calculate"

Result: Force ≈ 687 N

Explanation: Using F = G(m₁m₂)/r², this finds the gravitational force (weight) acting on the person. The result closely matches the standard weight: 70 kg × 9.8 m/s² ≈ 686 N. The slight difference (687 N vs 686 N) occurs because we're using the exact gravitational constant and Earth's precise mass, while g = 9.8 m/s² is an approximation.

Example 4: Calculate Momentum

Problem: A 0.5 kg ball has a momentum of 10 kg⋅m/s. What is its velocity?

Steps:

Select "Momentum" from the formula dropdown
Enter mass: 0.5 kg
Enter momentum: 10 kg⋅m/s
Leave velocity empty
Click "Calculate"

Result: Velocity = 20 m/s

Explanation: Using p = mv, we rearrange to v = p/m = 10 kg⋅m/s / 0.5 kg = 20 m/s. Momentum remains constant in collisions, making it a fundamental quantity in physics.

Example 5: Calculate Work Done

Problem: A 100 N force pushes a box 5 m along the floor at a 30° angle. How much work is done?

Steps:

Select "Work" from the formula dropdown
Enter force: 100 N
Enter distance: 5 m
Enter angle: 30°
Click "Calculate"

Result: Work ≈ 433 J

Explanation: Using W = Fdcos(θ), we get W = 100 N × 5 m × cos(30°) ≈ 433 J. The angle component shows that only the force component parallel to displacement contributes to work.

Classical Mechanics Calculator - Physics, Forces & Motion Solver

Newton's Second Law

Input Values

How to Use Classical Mechanics Calculator

Choose Your Formula

Enter Your Values

View Results

Calculator Features

Three Laws of Motion

Universal Gravitation

Energy Equations

Momentum & Impulse

Centripetal Force

Step-by-Step Solutions

Input Validation

Complete Function List

Common Calculations & Examples

Example 1: Calculate Force from Mass and Acceleration

Example 2: Calculate Kinetic Energy

Example 3: Calculate Gravitational Force

Example 4: Calculate Momentum

Example 5: Calculate Work Done

Tips for Using Classical Mechanics Calculator

Provide Enough Information

Check Your Units

Use Scientific Notation for Large Numbers

Review Step-by-Step Solutions

Frequently Asked Questions

What are the three laws of motion?

How do I find force using the Second Law?

What is the difference between kinetic and potential energy?

How does universal gravitation work?

What is momentum and why is it important?

How do I find work when force is at an angle?

Understanding Classical Mechanics Calculator

The Laws of Motion

Energy and Work

Momentum and Impulse

Universal Gravitation

Classical Mechanics Calculator - Physics, Forces & Motion Solver

Newton's Second Law

Input Values

How to Use Classical Mechanics Calculator

Choose Your Formula

Enter Your Values

View Results

Calculator Features

Three Laws of Motion

Universal Gravitation

Energy Equations

Momentum & Impulse

Centripetal Force

Step-by-Step Solutions

Input Validation

Complete Function List

Common Calculations & Examples

Example 1: Calculate Force from Mass and Acceleration

Example 2: Calculate Kinetic Energy

Example 3: Calculate Gravitational Force

Example 4: Calculate Momentum

Example 5: Calculate Work Done

Tips for Using Classical Mechanics Calculator

Frequently Asked Questions

Understanding Classical Mechanics Calculator

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