Two uniform discs in a vertical plane of masses M 1 and M 2 with radii R 1 , R 2 respectively have a thread wound about their circumferences, and are thus connected as shown in Fig.
The first disc has fixed frictionless horizontal axis of rotation through its center. Set up the equations to determine the acceleration of the center of mass of the second disc if it falls freely.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Let F be the tension in the thread, x 1 the distance of the center of mass of disc 2 from that of disc 1, and 
, 
the angular velocities of the discs, as shown in above fig. We have the equations of motion
M 2 
= M 2 g –F,
I 1 
= FR 1 ,
I 2 
= FR 2 ,
Where I 1 = m 1 R 1 2 /2, I 2 = m 2 R 2 2 /2. M 2 also have the constraint
= R 1 
+ R 2 
,
or 
= R 1 
+ R 2 
From the four equations the unknowns 
, 
, 
and F can be determined.
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