hw20 - khounvivongsy (sk27799) Homework 20 Weathers (17104)...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: khounvivongsy (sk27799) Homework 20 Weathers (17104) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A uniform disk of radius 3 . 9 m and mass 1 . 1 kg is suspended from a pivot 1 . 17 m above its center of mass. The acceleration of gravity is 9 . 8 m / s 2 . axis Find the angular frequency for small os- cillations. Correct answer: 1 . 13036 rad / s. Explanation: Basic Concepts The physical pendulum: = I = mg d sin = d 2 dt 2 so that the angular frequency for small oscil- lations (sin ) is = radicalbigg mg d I . Parallel axis theorem I = I + ma 2 Solution: We need the moment of inertia of the disk about the pivot point, which we call P. The moment of inertia of a uniform disk about its center is I disk = 1 2 mR 2 , but here the disk is rotating about P, a dis- tance d from the center of mass. The parallel axis theorem lets us move the axis of rotation a distance d : I P = 1 2 mR 2 + md 2 = m parenleftbigg R 2 2 + d 2 parenrightbigg . Then using the formula for the small angle oscillation frequency of a physical pendulum (see Basic Concepts above), we obtain = radicalBigg mg d I P = radicaltp radicalvertex radicalvertex radicalvertex radicalbt mg d m parenleftbigg R 2 2 + d 2 parenrightbigg or = radicaltp radicalvertex radicalvertex radicalvertex radicalbt g d R 2 2 + d 2 = radicaltp radicalvertex radicalvertex radicalvertex radicalbt (9 . 8 m / s 2 ) (1 . 17 m) (3 . 9 m) 2 2 + (1 . 17 m) 2 = 1 . 13036 rad...
View Full Document

This note was uploaded on 05/09/2010 for the course PHYS 1710 taught by Professor Weathers during the Spring '09 term at University of North Carolina Wilmington.

Page1 / 4

hw20 - khounvivongsy (sk27799) Homework 20 Weathers (17104)...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online