"""
Example 11: Rotational Dynamics (Phase 2.1)
Demonstrates rotational motion calculations including:
- Torque calculations
- Moment of inertia for various shapes
- Angular momentum
- Rotational kinetic energy
- Angular acceleration
No external services required - uses analytic provider.
"""
import asyncio
from chuk_mcp_physics.tools.rotational import (
calculate_torque,
calculate_moment_of_inertia,
calculate_angular_momentum,
calculate_rotational_kinetic_energy,
calculate_angular_acceleration,
)
async def main():
print("\n" + "=" * 70)
print("ROTATIONAL DYNAMICS EXAMPLES (Phase 2.1)")
print("=" * 70)
# Example 1: Torque - Wrench applying force
print("\n1. Torque Calculation - Wrench on Bolt")
print("-" * 70)
print("Scenario: 50 N force applied perpendicular to 80 cm wrench")
result = await calculate_torque(
force_x=50.0,
force_y=0.0,
force_z=0.0,
position_x=0.0,
position_y=0.0,
position_z=0.8, # 80 cm wrench
)
print("\nRESULTS:")
print(f" Torque vector: {result['torque']}")
print(f" Torque magnitude: {result['magnitude']:.1f} N⋅m")
print(f" Direction: {'Counter-clockwise' if result['torque'][1] > 0 else 'Clockwise'}")
# Example 2: Moment of Inertia - Various shapes
print("\n\n2. Moment of Inertia - Comparing Shapes")
print("-" * 70)
print("Comparing rotational inertia of different shapes with same mass")
shapes = [
("disk", {"mass": 5.0, "radius": 0.3}),
("sphere", {"mass": 5.0, "radius": 0.3}),
("hollow_sphere", {"mass": 5.0, "radius": 0.3}),
("rod", {"mass": 5.0, "length": 1.0}),
]
print(f"\n{'Shape':<20} {'Mass (kg)':<12} {'Radius/Length':<15} {'I (kg⋅m²)':<12}")
print("-" * 70)
for shape_name, params in shapes:
result = await calculate_moment_of_inertia(shape=shape_name, **params)
dimension = params.get("radius", params.get("length", 0))
print(
f"{shape_name:<20} {params['mass']:<12.1f} {dimension:<15.2f} {result['moment_of_inertia']:<12.4f}"
)
# Example 3: Angular Momentum - Spinning figure skater
print("\n\n3. Angular Momentum - Figure Skater Spin")
print("-" * 70)
print("Scenario: Skater spins with arms extended, then pulls arms in")
# Arms extended (approximated as disk)
I_extended = (
await calculate_moment_of_inertia(
shape="disk",
mass=60.0,
radius=0.8, # Arms extended
)
)["moment_of_inertia"]
# Arms pulled in
I_compact = (
await calculate_moment_of_inertia(
shape="disk",
mass=60.0,
radius=0.3, # Arms pulled in
)
)["moment_of_inertia"]
omega_initial = 2.0 # rad/s (slow spin)
# Calculate initial angular momentum
L_initial = await calculate_angular_momentum(
moment_of_inertia=I_extended,
angular_velocity_x=0.0,
angular_velocity_y=omega_initial,
angular_velocity_z=0.0,
)
# Conservation of angular momentum: L = I*ω = constant
# So: I_extended * ω_initial = I_compact * ω_final
omega_final = (I_extended * omega_initial) / I_compact
L_final = await calculate_angular_momentum(
moment_of_inertia=I_compact,
angular_velocity_x=0.0,
angular_velocity_y=omega_final,
angular_velocity_z=0.0,
)
print("\nArms Extended:")
print(f" I = {I_extended:.2f} kg⋅m²")
print(f" ω = {omega_initial:.2f} rad/s")
print(f" L = {L_initial['magnitude']:.2f} kg⋅m²/s")
print("\nArms Pulled In:")
print(f" I = {I_compact:.2f} kg⋅m²")
print(f" ω = {omega_final:.2f} rad/s ({omega_final / omega_initial:.1f}x faster!)")
print(f" L = {L_final['magnitude']:.2f} kg⋅m²/s")
print(
f"\nConservation check: ΔL = {abs(L_initial['magnitude'] - L_final['magnitude']):.6f} (should be ~0)"
)
# Example 4: Rotational Kinetic Energy - Flywheel
print("\n\n4. Rotational Kinetic Energy - Flywheel Energy Storage")
print("-" * 70)
print("Scenario: Industrial flywheel storing energy")
# Flywheel specs
mass = 500.0 # kg
radius = 1.0 # m
rpm = 3000 # revolutions per minute
omega = (rpm * 2 * 3.14159) / 60 # Convert to rad/s
moment_of_inertia = (await calculate_moment_of_inertia(shape="disk", mass=mass, radius=radius))[
"moment_of_inertia"
]
result = await calculate_rotational_kinetic_energy(
moment_of_inertia=moment_of_inertia, angular_velocity=omega
)
print("\nFlywheel Specifications:")
print(f" Mass: {mass:.0f} kg")
print(f" Radius: {radius:.1f} m")
print(f" Speed: {rpm:.0f} RPM ({omega:.1f} rad/s)")
print(f" Moment of inertia: {moment_of_inertia:.2f} kg⋅m²")
print("\nEnergy Storage:")
print(f" Rotational KE: {result['rotational_ke']:.0f} J")
print(f" In kWh: {result['rotational_ke'] / 3.6e6:.2f} kWh")
print(f" Equivalent to lifting {result['rotational_ke'] / 9.81:.0f} kg by 1 meter")
# Example 5: Angular Acceleration - Motor starting
print("\n\n5. Angular Acceleration - Electric Motor Startup")
print("-" * 70)
print("Scenario: Motor applies torque to accelerate rotor")
torque = 50.0 # N⋅m
I_motor = (await calculate_moment_of_inertia(shape="disk", mass=10.0, radius=0.15))[
"moment_of_inertia"
]
result = await calculate_angular_acceleration(torque=torque, moment_of_inertia=I_motor)
alpha = result["angular_acceleration"]
time_to_3000rpm = (3000 * 2 * 3.14159 / 60) / alpha # Time to reach 3000 RPM
print("\nMotor Specifications:")
print(f" Applied torque: {torque:.1f} N⋅m")
print(f" Rotor I: {I_motor:.4f} kg⋅m²")
print("\nAcceleration:")
print(f" Angular acceleration: {alpha:.1f} rad/s²")
print(f" Time to 3000 RPM: {time_to_3000rpm:.2f} seconds")
print(f" Linear analogy: Like accelerating at {alpha:.1f} m/s² at 1m radius")
# Example 6: Real-world application - Bicycle wheel
print("\n\n6. Real-World Application - Bicycle Wheel")
print("-" * 70)
print("Scenario: Analyzing bicycle wheel rotation")
wheel_mass = 2.0 # kg
wheel_radius = 0.35 # m (700c wheel)
speed_kmh = 25.0 # km/h
speed_ms = speed_kmh / 3.6
# Angular velocity: v = ωr, so ω = v/r
omega_wheel = speed_ms / wheel_radius
I_wheel = (
await calculate_moment_of_inertia(shape="cylinder", mass=wheel_mass, radius=wheel_radius)
)["moment_of_inertia"]
L_wheel = await calculate_angular_momentum(
moment_of_inertia=I_wheel,
angular_velocity_x=0.0,
angular_velocity_y=omega_wheel,
angular_velocity_z=0.0,
)
KE_wheel = await calculate_rotational_kinetic_energy(
moment_of_inertia=I_wheel, angular_velocity=omega_wheel
)
print("\nWheel Specifications:")
print(f" Mass: {wheel_mass:.1f} kg")
print(f" Radius: {wheel_radius:.2f} m")
print(f" Bike speed: {speed_kmh:.1f} km/h ({speed_ms:.2f} m/s)")
print(f" Wheel RPM: {omega_wheel * 60 / (2 * 3.14159):.0f}")
print("\nRotational Properties:")
print(f" Angular velocity: {omega_wheel:.1f} rad/s")
print(f" Moment of inertia: {I_wheel:.4f} kg⋅m²")
print(f" Angular momentum: {L_wheel['magnitude']:.2f} kg⋅m²/s")
print(f" Rotational KE: {KE_wheel['rotational_ke']:.1f} J")
print(" (This gyroscopic effect helps bike stay upright!)")
print("\n" + "=" * 70)
print("Phase 2.1 Complete! ✓")
print("=" * 70 + "\n")
if __name__ == "__main__":
asyncio.run(main())
