An object of mass m 1 =129.1 g undergoes constant circular motion with radius 65

Question

An object of mass m1=129.1 g undergoes constant circular motion with radius 65.6 cm on a flat frictionless table. It is connected by a massless string through a hole in the table to a larger object of mass m2=214.4 g. If, as the result, the hanging mass m2 is stationary, what is the angular speed of the rotating mass m1?

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CHEGG,

Please start with (show how you derive from) simple formulas (i.e. ac = (Vt2)/R = wVt = w2R and F = (mV2)/r and [arc length] = [angle in radians]/[t] etc.), and please show ALL your work. Thank you!

Explanation / Answer

Let T is acting on m2

if it is stationary

=> T = m2g

another mass m1 is on table ,if it is stationary

=> T = m1V^2/R OR m1W^2R ( centrifugal force balanced by tension)

=>  m1W^2R = m2g

=> W = sqrt ( (0.2144*9.8)/(0.1291*0.656)) = 4.98 rad/s

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