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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) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – Fnd all choices be±ore answering. 001 10.0 points The speed o± a moving bullet can be deter- mined by allowing the bullet to pass through two rotating paper disks mounted a distance 75 cm apart on the same axle. ²rom the angular displacement 23 . 2 o± the two bul- let holes in the disks and the rotational speed 1288 rev / min o± the disks, we can determine the speed o± the bullet. 23 . 2 v 1288 rev / min 75 cm What is the speed o± the bullet? Answer in units o± m / s. 002 10.0 points A bug is on the rim o± a 78 rev / min, 12 in . diameter record. The record moves ±rom rest to its Fnal angular speed in 2 . 79 s. ²ind the bug’s centripetal acceleration 1 . 5 s a±ter the bug starts ±rom rest. (1 in = 2.54 cm). Answer in units o± m / s 2 . 003 10.0 points A small wheel o± radius 2 . 2 cm drives a large wheel o± radius 12 . 9 cm by having their cir- cum±erences pressed together. I± the small wheel turns at 541 rad / s, how ±ast does the larger one turn? Answer in units o± rad / s. 004 10.0 points The angular position o± an object that rotates about a Fxed axis is given by θ ( t ) = θ 0 e βt , where β = 2 s 1 , θ 0 = 0 . 8 rad, and t is in seconds. What is the magnitude o± the total linear acceleration at t = 0 o± a point on the object that is 12 cm ±rom the axis? Answer in units o± cm / s 2 . 005 10.0 points Two balls o± equal mass at the bottom o± an incline are rolled upward without slipping at the same initial velocity. One ball is solid and the other is a thin-walled hollow ball. Which rolls higher up the incline be±ore coming to a stop? 1. The solid ball. 2. Both will roll to the same height. 3. Depends on the relative diameters o± the balls. 4. The hollow ball. 006 (part 1 o± 2) 10.0 points ²our particles with masses 6 kg, 6 kg, 3 kg, and 4 kg are connected by rigid rods o± neg- ligible mass as shown. The origin is centered on the mass in the lower-right corner. The rectangle is 7 m wide and 4 m long. x y 6 rad / s 4 m 7 m 6 kg 6 kg 3 kg 4 kg I± the system rotates in the xy plane about the z axis (origin, O ) with an angular speed o± 6 rad / s, calculate the moment o± inertia o± the system about the z axis. Answer in units o± kg · m 2 . 007 (part 2 o± 2) 10.0 points ²ind the rotational energy o± the system. Answer in units o± J.
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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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