Vertical Circular Motion Test. Calculus in 2D Know how to apply variable acceleration with vectors Understand how to apply core 3 calculus in questions.

Slides:

Advertisements

Similar presentations

What is Projectile Motion?

Advertisements

OBJECTIVES Ability to understand and define scalar and vector quantity. Ability to understand the concept of vector addition, subtraction & components.

01-1 Physics I Class 01 1D Motion Definitions.

02-1 Physics I Class 02 One-Dimensional Motion Definitions.

Motion Vectors. Displacement Vector  The position vector is often designated by.  A change in position is a displacement.  The displacement vector.

Position, Velocity and Acceleration Analysis

SPEED AND VELOCITY NOTES

Derivatives of Vectors Lesson Component Vectors Unit vectors often used to express vectors  P = P x i + P y j  i and j are vectors with length.

© Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Vectors.

Kinematics Vector and Scalar Definitions Scalar: a physical quantity that can be defined by magnitude (size) only. Vector: a physical quantity that can.

10.3 Vector Valued Functions Greg Kelly, Hanford High School, Richland, Washington.

Scalars and Vectors (a)define scalar and vector quantities and give examples. (b) draw and use a vector triangle to determine the resultant of two vectors.

10.2 Vectors and Vector Value Functions. Quantities that we measure that have magnitude but not direction are called scalars. Quantities such as force,

Travelling with vectors Basically a lesson where we recap and apply everything we’ve learnt so far.

UNIT 1: 1-D KINEMATICS Lesson 5: Kinematic Equations

1 Chapter 6: Motion in a Plane. 2 Position and Velocity in 2-D Displacement Velocity Average velocity Instantaneous velocity Instantaneous acceleration.

Ch. 3 Vectors & Projectile Motion. Scalar Quantity Described by magnitude only – Quantity Examples: time, amount, speed, pressure, temperature.

Projectiles Horizontal Projection Horizontally: Vertically: Vertical acceleration g  9.8 To investigate the motion of a projectile, its horizontal and.

NORMAL AND TANGENTIAL COMPONENTS

A jogger runs 145m in a direction 20

4.1 The Position, Velocity, and Acceleration Vectors 4.1 Displacement vector 4.2 Average velocity 4.3 Instantaneous velocity 4.4 Average acceleration 4.5.

Physics. Session Kinematics - 4 Session Opener X Y O X Y O X Y O X Y O Who is moving ? Who is at rest ? Everything is relative.

10.2 Vectors in the Plane Warning: Only some of this is review.

المحاضرة الخامسة. 4.1 The Position, Velocity, and Acceleration Vectors The position of a particle by its position vector r, drawn from the origin of some.

Lesson Average Speed, Velocity, Acceleration. Average Speed and Average Velocity Average speed describes how fast a particle is moving. It is calculated.

Resolve the vector into x & y components 40.0 m/s at 45 o SoW.

Kinematics in Two Dimensions. Section 1: Adding Vectors Graphically.

Relationship between time, displacement, velocity, acceleration. Kinematic.

Physics VECTORS AND PROJECTILE MOTION

Any vector can be written as a linear combination of two standard unit vectors. The vector v is a linear combination of the vectors i and j. The scalar.

2.1 Position, Velocity, and Speed 2.1 Displacement  x  x f - x i 2.2 Average velocity 2.3 Average speed  

S v t t Gradient of ST graph = Gradient of a VT graph = Area under a VT graph = Velocity Acceleration Displacement.

Vectors in the Plane Objectives: Define a vector What are the basic terms associated with vectors?

Chapter 3 Review Two-Dimensional Motion. Essential Question(s):  How can we describe the motion of an object in two dimensions using the one-dimensional.

Motion in Two Dimensions AP Physics C Mrs. Coyle.

Section 4.1 Speed & Velocity b What is motion? A change in the position of an object relative to another object (a reference point), which is assumed to.

Lesson Objective: Kinematics with Non Constant Acceleration WE CAN NO LONGER USE THE ‘SUVAT’ EQUATIONS !!

Chapter 3: Two-Dimensional Motion and Vectors. Objectives Define vectors and scalars. Understand simple vector operations like addition, subtraction,

Chapter 4 Lecture 6: Motion in 2D and 3D: I HW2 (problems): 2.70, 2.72, 2.78, 3.5, 3.13, 3.28, 3.34, 3.40 Due next Friday, Feb. 19.

Chapter 11: Motion Objectives: Identify frames of reference Distinguish between distance and displacement Interpret distance/time and speed/time graphs.

What is tested is the calculus of parametric equation and vectors. No dot product, no cross product. Books often go directly to 3D vectors and do not have.

Motion in Two and Three Dimensions Chapter 4. Position and Displacement A position vector locates a particle in space o Extends from a reference point.

AP Calculus Parametric/Vector Equations (1.4/11.) Arc Length (8.4) Created by: Bill Scott Modified by: Jen Letourneau 1.

Speed Velocity and Acceleration. What is the difference between speed and velocity? Speed is a measure of distance over time while velocity is a measure.

Chapter 3 Kinematics in two dimensions

Question 3 A car of mass 800kg is capable of reaching a speed of 20m/s from rest in 36s. Work out the force needed to produce this acceleration. m = 800kg v.

Variable Acceleration

Vectors Scalars and Vectors:

Calculate the Resultant Force in each case… Extension: Calculate the acceleration if the planes mass is 4500kg. C) B) 1.2 X 103 Thrust A) 1.2 X 103 Thrust.

The monkey and the hunter

Motion Chapter 11.

What is Projectile Motion?

Describing Motion.

What is Motion?.

Vectors Scalars and Vectors:

Physics VECTORS AND PROJECTILE MOTION

Introduction to Parametric Equations and Vectors

Derivatives of Vectors

NORMAL AND TANGENTIAL COMPONENTS

Section Indefinite Integrals

MechYr2 Chapter 8 :: Further Kinematics

Aim: How do we analyze the area under velocity-time graphs?

Motion in Space: Velocity and Acceleration

Physics VECTORS AND PROJECTILE MOTION

Section 9.4 – Solving Differential Equations Symbolically

Section Indefinite Integrals

Presentation transcript:

Vertical Circular Motion Test

Calculus in 2D Know how to apply variable acceleration with vectors Understand how to apply core 3 calculus in questions Be able to find a direction and magnitude

Recap DisplacementVelocityAcceleration You should recall from last lesson the how displacement, velocity and acceleration can be linked by differentiation and integration, if we are given an equation for one of them in terms of t. Don’t forget to consider the constant of integration +c when you are integration. You can use one set of values you know to work this out.

Var. Acc. in 2D In 2D we will consider having an equation for the position vector that describes the motion. r = xi + yj x and y can be a function of t to describe a particle in motion. We can just differentiate each component separately to find v and a. O i j x y

Magnitude and Direction Can be calculated using Pythagoras. Direction can be calculated using trigonometry. The magnitude of r is denoted by|r| or r. Similarly |v| or |a| can be used. O i j 4 2 r = 4i + 2j θ

Other ideas about direction We will try a couple of examples to deal with a few more things about direction. Such as : – finding when something is moving in the direction of i. – Finding when something is travelling North East (if i is defined as east and j is defined as north)

Example 1 The position vector of a particle is given by r = sin2ti +(t + cos 2t)j. a)Find an expression for the velocity of the particle at time t. b)Find the first value of t after t=0 for which the particle is moving in the direction of i. c)Show that the magnitude of the acceleration of the particle is constant.

Example 2 The position vector rkm, at time t hours of a boat relative to point O is given by r = (1 – cos3t)i – 2tj. Where i and j are unit vectors in the directions east and north respectively. Find the value of t for which the boat is moving south-east.

North (j) East (i) South East (i-j) Velocity is a multiple of (i-j)

Integration Example Find an expression for v and r in terms of t, given that a = (e -t )i + (1 – e -2t )j and v = 0 and r = 0 when t = 0

Question Time Try out the exam questions

Independent Study Differentiation Exercise B p 52 Q 1, 3, 5, 7 (solutions p 154) Integration Exercise C p56 Q 2, 3, 4 (solutions p 156)

Independent Study Try out the rest of exercise B/C p52-56