consider the gear ratio:
wfinal/wfirst=(.36/.12)/1.5
or wfinal=wfirst*3
and the same holds for angular acceleration
ok, when the larger turns once, the second turns three, so when the first rotates 3, the smaller rotates 9. The angular acceleration of the smaller is 3 times the larger.
at the end...
wfinal^2=2*acceleration*displacement
wfinal^2=2*1.5*3 * 3*3*2PI
solve for wfinal, then
linear speed is wfinal*radius
Two horizontal turntables are in contact with each other at their outer edges, and the static friction between them allows them to turn together (in opposite directions) without slipping. Thelarger turntable has a radius of 0.36m, and the smaller turntable a radius of 0.12m. The larger turntable accelerates from rest at a rate of 1.5rad/s2, and just when it completes its third revolution, a ball of clay that was (until now) stuck to the outer edge of the smaller turntable flies off. Find the speed of the ball of clay as it leaves the turntable.
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