There are three forces acting on the cylinder as it unrolls downwards,** i)** the force of gravity **mg** acting through its center of mass and **ii)** the tensions **T **each in the two pieces of string that hold it. Let the acceleration of the cylinder be **a**. Then we have,

**2TR**on the cylinder causing it to rotate. Let the angular acceleration of the cylinder be . Since the moment of intertia of the cylinder is , we have,

**(2)**and

**(3)**we can write,

**(4)**and

**(1)**we obtain,

**(5)**and

**(4)**we have,

**b)**At some instant of time if the cylinder is falling at a speed

**v**, its angualr velocity will be

**v/R**.The total energy of the cylinder at any given time is the sum of its translational kinetic energy and its rotational kinetic energy . At any given time the velocity of the cylinder if given by

**at**. Hence we have,

## 1 comment:

in question 1.254 the cart is going up with accelartion w0 so the force dowmwards should be

(g+w0),how can it be (g-w0)

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