Two uniform solid cylinders each rotating about its central(longitudinal) axis,
ID: 1915357 • Letter: T
Question
Two uniform solid cylinders each rotating about its central(longitudinal) axis, have the same mass of 4.92 kg and rotate with the same angular speed of 118rad/s, but they differ in radius .(a) what is the rotational kinetic energy of the smaller cylinder,of radius 0.116? (b) what is the rotational kinetic energy of the larger cylinder of radius 0.691m? (c)now imagine that the smaller cylinder uniformly expands(due to thermal expansion for example) to a new radius of 0.121 m. What is its angular velocity after the expansion? (hint:what quantity is conserved ).Explanation / Answer
Rotational kinetic energy K.E =( 1/2)Iw2 I - moment of inertia, w- angular speed I= (1/2)MR2 for a cylinder a)rotational KE of small cylinder = (1/2)(1/2)(4.92)(.116)2(118)2 = 230.45J b)rotational KE of large cylinder = (1/2)(1/2)(4.92)(.691)2(118)2 = 8.177J c) From law of conservation of angular mometum for a rotating body L angular momentum is constatnt L = Iw so I1w1 = I2w2 (1/2)(4.92)(.116)2(118)2 = (1/2)(4.92)(.121)2W2 W2 = 108rad/s so if the radius of small cylinder has increased then the new angular velocity is 108 rad/s
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