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# pai (acp655) - Homework 13 - orin - (58140) This print-out should have 10 questions. Multiple-choice questions may continue on the next column or...

Problem #6

Four particles with masses 6 kg, 6 kg, 3 kg,
and 4 kg are connected by rigid rods of neg-
ligible mass as shown. The origin is centered
on the mass in the lower-left corner. The
rectangle is 7 m wide and 4 m long.

If the system rotates in the xy plane about
the z axis (origin, O) with an angular speed
of 6 rad/s, calculate the moment of inertia of
the system about the z axis.
Answer in units of kg · m2.

pai (acp655) – Homework 13 – forin – (58140) 2 008 10.0 points A pendulum is made oF a rod oF mass 3 . 1 kg and length 3 . 1 m whose moment oF inertia about its center oF mass is 1 12 M L 2 and a thin cylindrical disk oF mass 1 . 7 kg and ra- dius 1 . 1 m whose moment oF inertia about its center oF mass is 1 2 M R 2 . 3 . 1 m 1 . 1 m 3 . 1 kg 1 . 7 kg ω What is the moment oF inertia oF the pen- dulum about the pivot point? Answer in units oF kg · m 2 . 009 10.0 points A circular disk with moment oF inertia 1 2 mR 2 , mass m and radius R is mounted at its center, about which it can rotate Freely. A light cord wrapped around it supports a weight mg . R I ω m T g ±ind the total kinetic energy oF the system when the weight is moving at a speed v . 1. K = 2 3 mv 2 2. K = 4 5 mv 2 3. K = 1 3 mv 2 4. K = 5 4 mv 2 5. K = 1 2 mv 2 6. K = 3 2 mv 2 7. K = 5 2 mv 2 8. K = mv 2 9. K = 3 4 mv 2 010 10.0 points A uniForm solid disk oF radius 1 . 87 m and mass 71 kg is Free to rotate on a Frictionless pivot through a point on its rim. 1 . 87 m Pivot IF the disk is released From rest in the position shown by the solid circle, what is the speed oF its center oF mass when the disk reaches the position indicated by the dashed circle? The acceleration oF gravity is 9 . 8 m / s 2 . Answer in units oF m / s.

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