AP Physics C: Mechanics Solver
Select a physics concept to calculate numeric solutions.
Kinematics (Constant Acceleration)
Newton's Second Law (F = ma)
Kinetic Energy (K = ½mv²)
Universal Gravitation (Fg)
Spring Period (SHM)
Torque (τ)
Final Velocity (v):
${vf.toFixed(4)} m/s
Displacement (Δx):
${d.toFixed(4)} m
`;
}
}
else if (mode === 'newton2') {
var m = parseFloat(document.getElementById('n_mass').value);
var acc = parseFloat(document.getElementById('n_acc').value);
if (isNaN(m) || isNaN(acc)) {
hasError = true;
} else {
var force = m * acc;
resultHTML = `
Net Force (F):
${force.toFixed(4)} N
`;
}
}
else if (mode === 'kinetic_energy') {
var m = parseFloat(document.getElementById('ke_mass').value);
var v = parseFloat(document.getElementById('ke_vel').value);
if (isNaN(m) || isNaN(v)) {
hasError = true;
} else {
var ke = 0.5 * m * Math.pow(v, 2);
resultHTML = `
Kinetic Energy (K):
${ke.toFixed(4)} J
`;
}
}
else if (mode === 'gravitation') {
var m1 = parseFloat(document.getElementById('g_m1').value);
var m2 = parseFloat(document.getElementById('g_m2').value);
var r = parseFloat(document.getElementById('g_r').value);
var G = 6.67430e-11;
if (isNaN(m1) || isNaN(m2) || isNaN(r) || r === 0) {
hasError = true;
} else {
var fg = (G * m1 * m2) / Math.pow(r, 2);
resultHTML = `
Gravitational Force (Fg):
${fg.toExponential(4)} N
`;
}
}
else if (mode === 'shm_spring') {
var m = parseFloat(document.getElementById('shm_m').value);
var k = parseFloat(document.getElementById('shm_k').value);
if (isNaN(m) || isNaN(k) || k === 0) {
hasError = true;
} else {
var period = 2 * Math.PI * Math.sqrt(m / k);
var freq = 1 / period;
resultHTML = `
Period (T):
${period.toFixed(4)} s
Frequency (f):
${freq.toFixed(4)} Hz
`;
}
}
else if (mode === 'torque') {
var r = parseFloat(document.getElementById('t_r').value);
var f = parseFloat(document.getElementById('t_f').value);
var theta = parseFloat(document.getElementById('t_theta').value);
if (isNaN(r) || isNaN(f) || isNaN(theta)) {
hasError = true;
} else {
// Convert degrees to radians
var rad = theta * (Math.PI / 180);
var torque = r * f * Math.sin(rad);
resultHTML = `
Torque (τ):
${torque.toFixed(4)} N·m
`;
}
}
var resultDiv = document.getElementById('result');
if (hasError) {
resultDiv.innerHTML = 'Please enter valid numeric values for all fields.';
} else {
resultDiv.innerHTML = resultHTML;
}
resultDiv.style.display = 'block';
}
Mastering AP Physics C: Mechanics Calculations
AP Physics C: Mechanics is a calculus-based physics course that requires a deep understanding of physical principles and the mathematical tools to apply them. While the exam requires deriving equations using calculus, verifying your numerical answers during homework or lab work is essential. This AP Physics C Mechanics Calculator serves as a multi-tool for the most common computational problems found in the curriculum.
How to Use This Calculator
This tool is designed with flexibility in mind, covering six major areas of the AP Physics C syllabus. Follow these steps to get accurate results:
- Select Calculation Mode: Use the dropdown menu to choose the specific physics concept you are working on (e.g., Kinematics, Torque, or Gravitation).
- Enter Variables: Input the known values from your problem statement. Ensure you use standard SI units (Meters, Kilograms, Seconds) to avoid conversion errors.
- Calculate: Click the blue button to compute the unknown variables.
Supported Calculations & Formulas
1. Kinematics (Uniform Acceleration)
Kinematics describes motion without considering its causes. When acceleration is constant, we use the "Big Four" equations. This calculator solves for final velocity and displacement.
v = v₀ + at
Δx = v₀t + ½at²
Δx = v₀t + ½at²
2. Newton's Second Law (Dynamics)
The foundation of classical mechanics. This mode calculates the net force required to accelerate a mass.
ΣF = ma
3. Work and Energy
The work-energy theorem is a powerful tool for solving problems that are difficult to approach with Newton's laws alone. This mode calculates translational Kinetic Energy.
K = ½mv²
4. Universal Gravitation
For celestial mechanics and satellite problems, Newton's Law of Universal Gravitation determines the attractive force between two massive bodies.
F_g = (G * m₁ * m₂) / r²
Where G ≈ 6.674 × 10⁻¹¹ N·m²/kg²
Where G ≈ 6.674 × 10⁻¹¹ N·m²/kg²
5. Simple Harmonic Motion (SHM)
Mass-spring systems are a staple of the AP Physics C exam. This calculator determines the period of oscillation based on mass and spring stiffness.
T = 2π√(m/k)
6. Rotational Motion (Torque)
Rotational dynamics introduces the concept of Torque, which is the rotational equivalent of Force. The angle of application is critical here.
τ = rF sin(θ)
Tips for AP Physics C Students
- Units Matter: Always convert grams to kilograms and centimeters to meters before calculating.
- Calculus Connection: Remember that while this calculator gives numerical answers, the AP exam requires you to know that Velocity is the derivative of Position (v = dx/dt) and Acceleration is the derivative of Velocity (a = dv/dt).
- Free Body Diagrams: Before using the Newton's Second Law calculator, always draw a Free Body Diagram (FBD) to ensure you are summing the correct forces.