Three objects lie in the x, y plane. Each rotates about the z axis with an angul

Question

Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 5.67 rad/s. The mass m of each object and its perpendicular distance r from the z axis are as follows: (1) m1 = 9.40 kg and r1 = 9.10 m, (2) m2 = 3.00 kg and r2 = 4.10 m, (3) m3 = 9.70 kg and r3 = 7.60 m. Find the tangential speed of (a) object 1, (b) object 2, and (c) object 3. (d) Determine the total kinetic energy of this system using the expression (e) Find the rotational kinetic energy of the system using the relation to verify that the answer is the same as that in (d).

Explanation / Answer

a) V 1 = 9.1*5.67 = 51.597 m/s,,,,,,,b)V2 = 5.67*4.1 = 23.247 ,,,,c) V3= 43.092 ,,,,, d) here total ke = rotational ke = 0.5( 9.4*9.1*9.1 + 3*4.1*4.1 + 9.7*7.6*7.6)*5.67*5.67 = 22437.36 J ,,,,,,,,,,,,e) 22437.36 J

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