Please show all work and make sure that the work can be easily to read and under

Question

Please show all work and make sure that the work can be easily to read and understand. Thank you very much.
= 20.0cm 4. A thin, cylindrical rod,4 He em long with mass m1 = 1.10 kg has d = 4.00 cm and miass M = 2.00 kg attached to one end. The arrangement vertical and stationary, with the ball at the top as shown. The combination pivot about the bottom end of the rod after being given a slight nudge. a ball of diameter e arrangement is originally is free to (a) What is the moment of inertia of the rod-and-ball system about the pivot? [4 ptsl At the instant the rod is horizontal, find (b) the rotational kinetic energy of the system and (3 pts (c) the angular speed of the rod and ball. [3 pts (b) the rotational kinetic energy of the system and 1g ptal

Explanation / Answer

part a )

by parallel axis theorem

Itotal = mL^2/3 + 2*MR^2/5 + M(L+d/2)^2

Itotal = 1.10 * (0.2m)^2/3 + 2*2 * ( 0.02)^2/5 + 2 * ( 0.2 + 0.02)^2

Itotal = 0.01467 + 3.2 x 10^-4 + 0.0968

Itotal = 0.11179 kg.m^2

part b )

change in potential energy = rotational kinetic energy

Mg(L+d/2) + mgL/2 = KErotational

2*9.8(0.2+ 0.02) + 1.1 * 9.8 * 0.2/2 = KE

KE = 5.39 J

part c)

KErotational = 1/2 *I*w^2

1/2*I*w^2 = 5.39

w = sqrt(2*5.39/0.11179)

w = 9.82 rad/s

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