A spool of radius 100m and mass 100kg has 100 grooves of radii 1m, 2m, ..., 100m. We use pulleys to suspend masses from the grooves as shown. The mass (i)kg is associated with the groove of radius (100-i)m.
Find the angular acceleration of the spool.
486(2Ï€*1+2Ï€*2.....2Ï€*100)Ï=100
2Ï€Ï100*1012=100
Ï=1101Ï€
Mass associated with groove of radius(100-i)m=2Ï€(100-i)1101Ï€
=2(100-i)101........(1)
Iα=(1*100+2*99+3*98....100*1)g
You can Calculate I using(1)
Anurag Ghosh Hmmm thanxx..
1161Well I have some questions..
1) Is there no friction at the ground surface?
2) Why tension will be equal to mg simply?
3) If let us take a scenario when there is only one groove at a radial distance of 50 m then whether we should take the MOI of whole wheel or just that groove as shown in the process??
Soumyadeep Basu MOI should be of the whole spool as any force creates an angular acceleration of the whole spool.