1. An experimental system consists of the solid cylinder of mass m and radius R

Question

1.      An experimental system consists of the solid cylinder of mass m and radius R that is able to rotate around its axis and is attached to the ceiling as shown. Two blocks of masses m1and m2 are connected by a light, non-stretchable rope as shown. There is no slippage of the rope on the cylinder. Find the angular acceleration a of the cylinder and the ratio of tension forces T1/T2 of the vertical portions of the rope while the blocks are moving. What is this ratio if mass of the cylinder m=0?

http://snag.gy/mpqcb.jpg

The diagram is above, listed as Problem 2.

An experimental system consists of the solid cylinder of mass m and radius R that is able to rotate around its axis and is attached to the ceiling as shown. Two blocks of masses m1 and m2 are connected by a light, non-stretchable rope as shown. There is no slippage of the rope on the cylinder. Find the angular acceleration a of the cylinder and the ratio of tension forces T1/T2 of the vertical portions of the rope while the blocks are moving. What is this ratio if mass of the cylinder m=0?

Explanation / Answer

let us consider the mass m1 moving down and mass m2 moving up

consider balancing of torque of pulley

we get

(T1-T2)*R=I*alpha ---------------------i

where I=m*R^2/2

and force balance of mass m1 we get

(m1g-T1)=m1*a ----------------------ii

where a=R*alpha ( since no slip condition)

force balance for mass m2

we get

(T2-m2g)=m2*a (a=R*alpha)----------------iii

accelaration of both a=mass is same since one string is connected and it is inextensible

thus solving i ii iii we get

alpha=(m1-m2)*g/((m/2+(m1+m2))*R)

and T1/T2=

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