The Atwood machine (or Atwood's machine) was invented in 1784 by the English mathematician George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics.
The ideal Atwood machine consists of two objects of mass and , connected by an inextensible massless string over an ideal massless pulley.
Both masses experience uniform acceleration. When , the machine is in neutral equilibrium regardless of the position of the weights.
An equation for the acceleration can be derived by analyzing forces. Assuming a massless, inextensible string and an ideal massless pulley, the only forces to consider are: tension force (), and the weight of the two masses ( and ). To find an acceleration, consider the forces affecting each individual mass. Using Newton's second law (with a sign convention of derive a system of equations for the acceleration ().
As a sign convention, assume that a is positive when downward for and upward for . Weight of and is simply and respectively.
Forces affecting m<sub>1</sub>: Forces affecting m<sub>2</sub>: and adding the two previous equations yields and the concluding formula for acceleration
The Atwood machine is sometimes used to illustrate the Lagrangian method of deriving equations of motion.