What Is the Atwood Machine?
Atwood's machine [1] , also translated as Atwood or Atwood, is an English pastor, mathematician and physicist George Atwood's "About Objects" published in 1784. [2] proposed in the article "Straight Motion and Rotation", a mechanism for measuring acceleration and verifying the laws of motion. This machine is now often used in school teaching to explain the principles of physics, especially mechanics. [3]
- Its basic structure is to suspend two masses of equal mass on both ends of a light rope that crosses a fixed pulley. When another small mass is attached to a mass, the mass will accelerate and slide down from a standstill. The add-on block automatically disengages, and the system moves at a constant speed. The acceleration of gravity can be obtained by measuring this movement speed. An ideal Atwood machine consists of two object masses m 1 and m 2 , and an ideal and weightless pulley connected by a weightless, inelastic rope. When m 1 = m 2 , the machine is in a state of force balance. When m 2 > m 1 , both objects are subject to the same constant acceleration.
- Atwood machines can be used to prove Newton's second law.
- If the weight difference between m 1 and m 2 is small, the moment of inertia ( I ) caused by the radius of the pulley ( r ) cannot be ignored.
- The angular acceleration of the pulley can be obtained from the following formula:
- In this case, the total moment of the system is: