The pulleys in figure (10-E6) are identical, each having a radius R and moment of inertia I. Find the acceleration of the block M.

The acceleration of the block M is

Given

The blocks are of “m” and “M” masses, with radius of r pulley and moment of Inertia “I”

Formula Used

The formula used to find the acceleration of the mass pulled/pushed is determined by the second law of Newton when the Force/Tension applied is equivalent to the product of mass and acceleration

where

is the force of the mass in terms of tension, is the acceleration and m is the mass of the block.

Explanation

The tension produced by the larger masses M is given and the smaller mass m is given as , and the tension between the pulley is therefore, the tension on both the masses are:

……1

and

……2

Now the acceleration of the pulley after deriving from angular acceleration is

Putting the value of tensions and inertia into the equation gives us acceleration as