Lecture 17

# Lecture 17 - Lecture 17 CURVILINEAR MOTION: GENERAL &amp;...

This preview shows pages 1–5. Sign up to view the full content.

Dynamics: Lecture Notes for Sections 12.4-12.6 1 Lecture 17 CURVILINEAR MOTION: GENERAL & RECTANGULAR COMPONENTS MOTION OF A PROJECTILE Section 12.4-12.6 Ehab Zalok 2 CURVILINEAR MOTION: GENERAL & RECTANGULAR COMPONENTS Today’s Objectives : Students will be able to: 1. Describe the motion of a particle traveling along a curved path. 2. Relate kinematic quantities in terms of the rectangular components of the vectors.

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

View Full Document
Dynamics: Lecture Notes for Sections 12.4-12.6 2 3 APPLICATIONS The path of motion of each plane in this formation can be tracked with radar and their x, y, and z coordinates (relative to a point on earth) recorded as a function of time. How can we determine the velocity or acceleration of each plane at any instant? Should they be the same for each aircraft? 4 APPLICATIONS (continued) A roller coaster car travels down a fixed, helical path at a constant speed. How can we determine its position or acceleration at any instant? If you are designing the track , why is it important to be able to predict the acceleration ( F = ma ) of the car?
Dynamics: Lecture Notes for Sections 12.4-12.6 3 5 GENERAL CURVILINEAR MOTION (Section 12.4) A particle moving along a curved path undergoes curvilinear motion . Since the motion is often three-dimensional, vectors are used to describe the motion. A particle moves along a curve defined by the path function, s. The position of the particle at any instant is designated by the vector r = r (t). Both the magnitude and direction of r may vary with time. If the particle moves a distance Δ s along the curve during time interval Δ t, the displacement is determined by vector subtraction : Δ r = r’ - r 6 VELOCITY Velocity represents the rate of change in the position of a particle. The average velocity of the particle during the time increment Δ t is v avg = Δ r / Δ t . The instantaneous velocity is the time-derivative of position v = d r /dt . The velocity vector , v , is always tangent to the path of motion. The magnitude of v is called the speed . Since the arc length Δ s approaches the magnitude of Δ r as t 0, the speed can be obtained by differentiating the path function (v = ds/dt). Note that this is not a vector!

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

View Full Document
Dynamics: Lecture Notes for Sections 12.4-12.6 4 7 ACCELERATION Acceleration represents the rate of change in the velocity of a particle. If a particle’s velocity changes from v to v over a time increment Δ t, the average acceleration during that increment is: a avg = Δ v / Δ t = ( v - v’ )/ Δ t The instantaneous acceleration is the time- derivative of velocity: a = d v /dt = d 2 r /dt 2 A plot of the locus of points defined by the arrowhead of the velocity vector is called a hodograph .
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/28/2011 for the course MATH 101 taught by Professor Duke during the Spring '11 term at University of Ottawa.

### Page1 / 14

Lecture 17 - Lecture 17 CURVILINEAR MOTION: GENERAL &amp;...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online