Classical Mechanics forms the bedrock of physics, explaining how objects move and interact under the influence of forces. With Moogle Math’s Physics Mechanics Solver, you can analyze motion, predict trajectories, and solve problems involving energy, momentum, and rotational dynamics with unmatched precision.
Kinematics
Example: Calculate the displacement of an object moving with a constant acceleration \(a = 3 \, \text{m/s}^2\) for \(t = 5 \, \text{s}\).
Input: kinematics(displacement, initial_velocity=0, acceleration=3, time=5)
Newton’s Laws of Motion
Example: Determine the net force acting on an object with mass \(m = 5 \, \text{kg}\) accelerating at \(a = 2 \, \text{m/s}^2\).
Input: newtons_laws(force, mass=5, acceleration=2)
Energy and Work
Example: Calculate the work done by a force \(F = 10 \, \text{N}\) over a displacement of \(d = 4 \, \text{m}\).
Input: work_done(force=10, displacement=4)
Momentum and Impulse
Example: Find the final velocity of an object after an impulse \(I = 20 \, \text{Ns}\) is applied.
Input: momentum(final_velocity, mass=4, impulse=20)
Rotational Motion
Example: Calculate the angular velocity of a wheel after \(t = 3 \, \text{s}\) with an angular acceleration of \(\alpha = 2 \, \text{rad/s}^2\).
Input: rotational_motion(angular_velocity, initial_velocity=0, angular_acceleration=2, time=3)
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Example: An object is thrown vertically upward with an initial velocity of v=20 m/sv = 20 \, \text{m/s}. Find its maximum height.
Input: projectile_motion(max_height, initial_velocity=20, gravity=9.8)
Example: Calculate the centripetal force for an object of mass m=2 kgm = 2 \, \text{kg} moving at v=10 m/sv = 10 \, \text{m/s} in a circle of radius r=5 mr = 5 \, \text{m}.
Input: circular_motion(centripetal_force, mass=2, velocity=10, radius=5)
Example: A ball of mass m1=2 kgm_1 = 2 \, \text{kg} moving at v1=3 m/sv_1 = 3 \, \text{m/s} collides elastically with another ball of mass m2=4 kgm_2 = 4 \, \text{kg} at rest. Find their velocities after collision.
Input: elastic_collision(m1=2, v1=3, m2=4, v2=0)
Example: Determine the period of a spring-mass system with k=200 N/mk = 200 \, \text{N/m} and m=2 kgm = 2 \, \text{kg}.
Input: harmonic_motion(period, spring_constant=200, mass=2)
Example: Calculate the gravitational force between two masses m1=5 kgm_1 = 5 \, \text{kg} and m2=10 kgm_2 = 10 \, \text{kg} separated by a distance of r=2 mr = 2 \, \text{m}.
Input: gravitational_force(m1=5, m2=10, distance=2)