A small 90 gram block is attached to a massless cord passing through a small hol

Question

A small 90 gram block is attached to a massless cord passing through a small hole in frictionless, horizontal oriented table top surface as shown in the figure.

A small 90 gram block is attached to a massless cord passing through a small hole in a frictionless horizontally oriented table top surface, as sho n in the figure. The block is initially revolving th velocit v = 70 cm/s, on a radius of r_0 40 cm from the hole. If the magic hand shown shortens the radius of revolution to r_final 10 cm, calculate the final angular frequency Omega_final, and the final tangential velocity, V_final. Select one O a. Omega f 40 rad/sec, V f 4 m/s O b. Omega t 21 rad/sec, V t- 2.1 m/s c. Omega-f = 18 radsec.V-f-1.05 ms d. Omega-t = 10 rad/sec. VT = 0.5 m/s O

Explanation / Answer

from the angular momentum conservation

m1*v1*r1 = m2*v2*r2

given

m1 = m2 = 90g

v1 = 70cm/s = 0.7m/s

r1 = 40cm = 0.4m

r2 = 10cm= 0.10 m

put all values in above equation

0.7*0.4 = 0.10*v2

v2 = 2.8 m/s

angular frequency w2 = v2/r2 = 2.8/0.1 = 28 rad/s

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