Examples by Topic

Classical Mechanics

Classical Mechanics

Basic Mechanics

do a Newton's second law computation

force m=150g, a=50cm/s^2

compute momentum

momentum m=12kg, v=30m/s

compute impulse

F=5 Newtons, t=8 seconds

compute torque

3m, 1N, torque?

compute centripetal acceleration

centripetal acceleration, 30mph, 500 ft

compute rolling motion

rolling motion, v=3m/s, omega=40 rad/s

find equations of particle motion

free particle

damped harmonic oscillator with forcing

analyze a harmonic oscillator

damped harmonic oscillator with forcing

find equations associated to a harmonic oscillator

damped sinusoidal driven harmonic oscillator (physical system)

calculate engineering strain

cauchy strain with final length 2m

nominal strain e with final length 2m and original length 1.99m

find the stress on a cylinder

diameter 5mm and force 2N, what is the mechanical stress

determine the poisson ratio value for a deformation

poisson effect with original length 2m and width 1m


compute mechanical work

mechanical work calculator

work F=30N, d=100m

work at constant acceleration

specify an angle between force and displacement

mechanical work, 30 degrees

work, F=3N, d=6m, theta=25 degrees

compute rotational work

rotational work

work, tau=9N m, theta=5 degrees

Motion on an Inclined Plane

compute motion of a block on an inclined plane

a 2.1kg block slides down an inclined plane

compute motion of a round object on an inclined plane

ball on incline for 10 seconds

hollow cylinder slides and rolls down a gradient of 0.3, muk=0.3

find the Hamiltonian of a system

inclined plane Hamiltonian


analyze an elastic collision in one dimension

elastic collision m1=3kg, v1i=4m/s, m2=2kg, v2i=-1m/s

analyze an elastic collision in two dimensions

2d elastic collision, theta=40deg

analyze motion of a simple pendulum


analyze motion of a spring pendulum

spring pendulum l0=0.12m, li=0.24m, thetai=80deg

find the Lagrangian of a system

Lagrangian of a coupled pendulum system

Motion of a Top

analyze the motion of a symmetric top

motion of a symmetric top

find the equations of motion

equations of motion for a symmetric top

Rocket Motion

analyze motion of a rocket

classical rocket equation

do a gravitation calculation

gravitation calculation

find equations associated with the two-body problem

two-body problem

compute time to fall

time to fall 1000ft

compute work done against gravity

work against gravity, height = 2 meters