Examples for

Dynamics

The field of dynamics studies forces and torques and their effect on motion. Use Wolfram|Alpha to compute the motion of objects subject to torques and forces. Explore the mechanical advantage of simple machines and calculate the work done by applied forces.

Basics

Calculate the motion of objects under the influence of forces and torques.

Do a Newton's second law computation:

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

Compute impulse:

F=5 Newtons, t=8 seconds

Compute rolling motion:

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

Simple Machines

Determine the mechanical advantage of the classical simple machines such as the screw, wedge and lever.

Compute mechanical advantages of simple machines:

mechanical advantage of a lever
pulley system, n=4

Motion on an Inclined Plane

Analyze the equations of motion of an object 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

Work

Calculate various forms of work such as rotational, force over distance and force applied at an angle.

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

RELATED EXAMPLES

  • Gravity
  • Kinematics
  • Oscillations & Waves
  • Physical Principles

    • Circular Motion

    Calculate motion and forms of acceleration constrained within a circular arc.

    Compute torque:

    3m, 1N, torque?

    Compute centripetal acceleration:

    centripetal acceleration, 30mph, 500 ft

    Compute the Coriolis acceleration in a rotating frame of reference:

    Coriolis effect 5mph 30rpm