Question

Two metal disks, one with radius R1 = 2.60cm and mass M1 = 0.700kg and the other with radius R2 = 5.05cmand mass M2 = 1.55kg , are welded together and mounted on a frictionless axis through their common center. A light string is wrapped around the edge of the smaller disk and a 1.40kg block is suspended from the free end of the string.

Part A

What is the magnitude of the downward acceleration of the block after it is released?

Take the free fall acceleration to be 9.80m/s2.

Part B

Repeat the calculation of part (a), this time with the string wrapped around the edge of the larger disk.

Take the free fall acceleration to be 9.80m/s2.

Answer 1

a)I=(0.700*0.0260^2+1.55*0.0505^2)/2

=0.00221 kg m^2

A FBD of the hanging mass
1.40*9.8-T=1.40*a

where T is the tension

A FBD of the disks
T*0.0260=0.00221*a/0.0260

T=0.326a

combine and solve for a
1.40*9.8-T=1.40*a
13.72-T=1.40a

13.72-0.326a=1.40a

7.94 m/s^2

b) if the system is frictionless, they shud fall down at the same acceleration which is 7.94 m/s^2.. bcz the mass does not effect its acceleration.. and the acceleration depends on the gravity.. hope this helps..