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(Solved): [Practice 6] Small balls 1 and 2 with a mass of 2m and m, respectively, are hung on either side of a ...



[Practice 6] Small balls 1 and 2 with a mass of

2m

and

m

, respectively, are hung on either side of a pulley (inner ring radius

2R

, outer ring radius

4R

) with the moment of inertia

I

as shown in the figure. Initially, the difference in height between the two small balls is

L

and the ball 1 is supported by hand. (a) Once the ball 1 is released, the balls start moving and the pulley starts rotating. The acceleration of ball 1 and 2 is

a_(1)

and

a_(2)

, and tension of thread for ball 1 and 2 is

T_(1)

and

T_(2)

, respectively. Make the equation of motion for ball 1 and 2 , and the equation of rotational motion for the pulley. Also, express

a_(1)

and

a_(2)

using angular acceleration

\alpha

of the pulley. (b) If

I=6mR^(2)

, find

a_(1),a_(2),T_(1),T_(2)

, and

\alpha

(c) Find the time

t

until balls 1 and 2 reach the same height.



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