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

pai (acp655) – Homework 13 – orin – (58140) 1 This print-out should have 10 questions.

Multiple-choice questions may continue on the next column or page – nd all choices before answering. 001 10.0 points The speed of 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. From the angular displacement 23 .2 ◦ of the two bul- let holes in the disks and the rotational speed 1288 rev /min of the disks, we can determine the speed of the bullet. 23 .2 ◦ v 1288 rev /min 75 cm What is the speed of the bullet?

Answer in units of m /s. 002 10.0 points A bug is on the rim of a 78 rev /min, 12 in .

diameter record. The record moves from rest to its nal angular speed in 2 .79 s.

Find the bug’s centripetal acceleration 1 .5 s after the bug starts from rest. (1 in = 2.54 cm). Answer in units of m /s2 .

003 10.0 points A small wheel of radius 2 .2 cm drives a large wheel of radius 12 .9 cm by having their cir- cumferences pressed together.

If the small wheel turns at 541 rad /s, how fast does the larger one turn? Answer in units of rad /s.

004 10.0 points The angular position of an ob ject that rotates about a xed axis is given by (t) = 0 e t , where = 2 s − 1 , 0 = 0 .8 rad, and tis in seconds.

What is the magnitude of the total linear acceleration at t= 0 of a point on the ob ject that is 12 cm from the axis? Answer in units of cm /s2 . 005 10.0 points Two balls of equal mass at the bottom of 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 before coming to a stop?

1. The solid ball.

2. Both will roll to the same height.

3. Depends on the relative diameters of the balls.

4. The hollow ball. 006 (part 1 of 2) 10.0 points 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-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 If the system rotates in the xyplane about the zaxis (origin, O) with an angular speed of 6 rad /s, calculate the moment of inertia of the system about the zaxis.

Answer in units of kg ·m 2 . 007 (part 2 of 2) 10.0 points Find the rotational energy of the system. Answer in units of J. pai (acp655) – Homework 13 – orin – (58140) 2 00810.0 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 12M 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 2M R 2 .

3 .1 m 1 .1 m 3 .1 kg 1.7 kg 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 m R 2 , mass mand radius Ris mounted at its center, about which it can rotate freely.

A light cord wrapped around it supports a weight m g. R I m T g Find the total kinetic energy of the system when the weight is moving at a speed v.

1. K =2 3m v 2 2.

K =4 5m v 2 3. K =1 3m v 2 4. K =5 4 m v 2 5. K =1 2 m v 2 6. K =3 2m v 2 7. K =5 2m v 2 8. K =m v 2 9. K =3 4m v 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 /s2 .

Answer in units of m /s.