3.) The moment of inertia of the carousel with radius R 4.5m is L 1874 kg m2. ca

Question

3.) The moment of inertia of the carousel with radius R 4.5m is L 1874 kg m2. carousel Becky has mass m F 56 kg and stands on the carousel at the radius ro E 4.0 m. a) The carousel completes a full revolution every 25 seconds. Find the total angular momentum and the total rotational kinetic energy of the entire system carousel plus Beckyl b) Becky now walkes towards the center and stops at the radius r 3.2 m. How long does it take to complete a full revolution when she is at r 3.2 m? c The carousel completes one quarter of a revolution, while Becky walks from ro J 4.0 m to r 3.2 m. Find the (average) torque exerted by Becky on the carousel.

Explanation / Answer

3) Given time period T = 25

So, its angular speed w = 2x3.14/25 = 0.2512 rad/s

Moment of inertia of Becky I1 = mxrxr = 56x4x4 = 896

So, total moment of inertia I = 896 + 1874 = 2770

So, total angular momentum = Ixw = 2770x0.2512 = 695.8 Ans

Total kinetic energy E = 1/2xIxwxw = 0.5x2770x0.2512x0.2512 = 87.4 joule Ans

b) When Becky moves to the radius of 3.2 m,

then his moment of inertia = 56x3.2x3.2 = 573.44

So now total moment of Inertia I2 = 1874+573.44 = 2447.44

So, now applying conservation of angular momentum,

Iw = I2w2

w2 = Iw/I2 = 695.8/2447.44 = 0.2842

So, new time period T1 = 2x3.14/w2 = 2x3.14/0.2842 = 22 s Ans

For moving from 4 to 3.2m, becky takes one quarter cycle, means it takes ( 25+22)/4 = 5.875 sec

And change in angular momentum of carosuel = 1874(0.2842-0.2512) = 61.842 Ans

Please put other quaestions seperately, then I will solve them all.

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