Circular Motion – Sect. 4.4: Uniform Circular Motion. Sect. 4.5: Tangential & Radial Acceleration.

Slides:

Advertisements

Similar presentations

Uniform circular motion – Another specific example of 2D motion

Advertisements

Circular Motion. Position on a Circle  Motion in a circle is common.  The most important measure is the radius ( r ).  The position of a point on the.

As the ball revolves faster, the angle increases

General Physics 1, Lec 8 By/ T.A. Eleyan 1 Lecture 8 Circular Motion & Relative Velocity.

Week.  Student will: centripetal accelerationcentripetal force  Solve problems involving centripetal acceleration and centripetal force.

Uniform Circular Motion Physics 6A Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.

Uniform Circular Motion

Circular Motion and Other Applications of Newton’s Laws

CIRCULAR MOTION.

Circular Motion Kinematics 8.01 W04D1. Today’s Reading Assignment: W04D1 Young and Freedman: 3.4; Supplementary Notes: Circular Motion Kinematics.

Rotational Motion = Uniform Circular Motion r r v2v2 v1v1 7v7v 2 2 a b Chord ab c d e f Using similar triangles abc def Where r is.

Uniform Circular Motion

1 Chapter (6) Circular Motion. 2 Consider an object moving at constant speed in a circle. The direction of motion is changing, so the velocity is changing.

Centripetal Acceleration/Force. Centripetal Force/Acceleration Definition Centripetal force: Centripetal force: Any force that causes curved path motion.

Cutnell/Johnson Physics 7th edition Reading Quiz Questions

ROTATIONAL MOTION Uniform Circular Motion

Circular Motion. Uniform Circular Motion Motion of an object at constant speed along a circular path.

Centripetal Motion Motion towards the center of a circle.

Uniform Circular Motion. What is uniform circular motion? 4 Movement of an object at constant speed around a circle with a fixed radius 4 Can the velocity.

Circular Motion Chapter 9. Circular Motion Axis – is the straight line around which rotation takes place. Internal Axis - is located within the body of.

CHAPTER 6 : CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS

7-3 Circular Motion. As an object travels in uniform circular motion Its tangential speed remains constant The direction of its velocity is constantly.

المحاضرة الثالثة Circular Motion There are two types of circular motion:- 1- Uniform circular motion 2- Non uniform circular motion 1- Uniform circular.

How do you relate the angular acceleration of the object to the linear acceleration of a particular point? There are actually two perpendicular components.

Objectives  Explain why an object moving in a circle at a constant speed is accelerated.  Describe how centripetal acceleration depends upon the object’s.

Centripetal Acceleration is a vector quantity because it has both direction and magnitude. Centripetal Acceleration is defined as an acceleration experienced.

Circular motion Objectives: understand that acceleration is present when the magnitude of the velocity, or its direction, or both change; understand that.

Circular Motion Deriving the formula for centripetal acceleration.

CIRCULAR MOTION. WHAT IS UNIFORM CIRCULAR MOTION The motion of an object in a circle at constant speed. However, direction and therefore velocity are.

Universal Force of Gravity and Circular Motion Unit 5.

Uniform Circular Motion Definition: the motion of an object in a circular path with a constant speed Homework: Read pages 153 – 156 P 156 Answer questions:

CIRCULAR MOTION. CRSHS, III- Galileo, Physics Teacher: Mrs. Maria Ruth Edradan Group 4task: Catulaypowerpoint Yeelaptop Pomoyinfo Matildoinfo Bononoinfo.

Circular Motion A brief intro.. Uniform Circular Motion UCM is the movement of an object or particle trajectory at a constant speed around a circle with.

Uniform Circular Motion. Acceleration When an object moves at a constant speed in a circular path, it is constantly changing direction – accelerating.

Circular Motion = the movement of an object at constant speed around a circle with fixed radius Axis – straight line around which rotation takes place.

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.

Circular Motion By: Heather Britton. Circular Motion Uniform circular motion - the motion of an object traveling at constant speed along a circular path.

Chapter Uniform Circular Motion  Uniform circular motion is the motion of an object traveling at a constant (uniform) speed on a circular path.

Chapter 4 MOTION IN TWO DIMENSIONS. Two dimensions One dimension Position O x M x x y M Path of particle O x y.

Sect. 5-2: Uniform Circular Motion. The motion of a mass in a circle at a constant speed. Constant speed  The Magnitude (size) of the velocity vector.

Set 4 Circles and Newton February 3, Where Are We Today –Quick review of the examination – we finish one topic from the last chapter – circular.

C H A P T E R 5 Dynamics of Uniform Circular Motion.

Proportionality between the velocity V and radius r

Dynamics of Uniform Circular Motion Uniform Circular Motion Centripetal Acceleration Centripetal Force Satellites in Circular Orbits Vertical Circular.

Circular Motion. Speed/Velocity in a Circle Consider an object moving in a circle around a specific origin. The DISTANCE the object covers in ONE REVOLUTION.

Circular Motion r v F c, a c. Centripetal acceleration – acceleration of an object in circular motion. It is directed toward the center of the circular.

1 Uniform Circular Motion SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. g. Measure and calculate.

Circular Motion Chapter 9 in the Textbook Chapter 6 is PSE pg. 81.

L12-s1,7 Physics 114 – Lecture 12 Chapter 5 Circular Motion; Gravitation We have so far considered motion along a straight line – F net acts along line.

Chapter 4 Motion in two and three dimensions. 4.7: Uniform Circular Motion The speed of the particle is constant A particle travels around a circle/circular.

Uniform circular motion is the motion of an object traveling at a constant speed on a circular path. Uniform Circular Motion.

Circular Motion AP Physics Mrs Coyle. Earth rotates about its axis Satellite revolves about the earth. Rotation vs Revolution.

4.1 Motion in a Circle p. 120 Gravity and Motion The force that keeps a body firmly attached to the ground is the same force that keeps the Moon in orbit.

Circular Motion Chapter 7.3. Motion & Forces What you already know: –Velocity – a measure of the change in displacement (distance with direction. –Mass.

Do Now Which of the following objects is accelerating: a. A car slowing down. b. A free fall object momentarily stopped at its max height. c. A ball tied.

Chapter 5 Dynamics of Uniform Circular Motion. 5.1 Uniform Circular Motion DEFINITION OF UNIFORM CIRCULAR MOTION Uniform circular motion is the motion.

UNIFORM CIRCULAR MOTION Centripetal force. UNIFORM CIRCULAR MOTION  Motion at a constant speed around a circle with a constant radius. V Fc Ac.

Dynamics of Uniform Circular Motion  An object moving on a circular path of radius r at a constant speed, V  Motion is not on a straight line, the direction.

Uniform Circular Motion. 4 dXxQ7o dXxQ7o.

Circular Motion and the Law of Universal Gravitation.

SACE Stage 2 Physics Circular Motion.

PHY 151: Lecture 4B 4.4 Particle in Uniform Circular Motion 4.5 Relative Velocity.

Circular Motion Physics 1 Prepared by Vince Zaccone

Figure shows a car moving in a circular path with constant linear speed v. Such motion is called uniform circular motion. Because the car’s.

Uniform Circular Motion

Chapter 7 Objective Solve problems involving centripetal acceleration.

Uniform Circular Motion

Uniform Circular Motion

Chapter 5: Circular Motion; Gravitation

Circular Motion r v Fc, ac.

Presentation transcript:

Circular Motion – Sect. 4.4: Uniform Circular Motion. Sect. 4.5: Tangential & Radial Acceleration

Uniform Circular Motion Motion of a mass in a circle at constant speed. Constant speed  The Magnitude (size) of the velocity vector v is constant. BUT the DIRECTION of v changes continually! v  r v = |v| = constant r r

For a mass moving in circle at constant speed. Acceleration  Rate of Change of Velocity a = (Δv/Δt) Constant Speed  The Magnitude (size) of the velocity vector v is constant. BUT the DIRECTION of v changes continually!  An object moving in a circle undergoes acceleration!! v = |v| = constant

Centripetal (Radial) Acceleration Consider motion in a circle from A to point B. The velocity v is tangent to the circle. a = lim Δt  0 (Δv/Δt) = lim Δt  0 [(v 2 - v 1 )/(Δt)] As Δt  0, Δv   v & Δv is in the radial direction  a  a c is radial!

 a  a c is Radial!! Similar Triangles  (Δv/v) ≈ (Δℓ/r) As Δt  0, Δθ  0, A  B

(Δv/v) = (Δℓ/r)  Δv = (v/r)Δℓ Note that the acceleration (radial) is a c = (Δv/Δt) = (v/r)(Δℓ/Δt) As Δt  0, (Δℓ/Δt)  v and Magnitude: a c = (v 2 /r) Direction: Radially inward! “Centripetal”  “Towards the Center” Centripetal Acceleration is acceleration towards the center.

A typical figure for a particle moving in uniform circular motion, radius r (speed v = constant) is shown here: Velocity vector v is always Tangent to the circle!! a = a c = Centripetal Acceleration a c is Radially Inward always!  a c  v always!! Magnitude: a c = (v 2 /r)

Period & Frequency Consider again a particle moving in uniform circular motion of radius r (speed v = constant) Description in terms of period T & frequency f: Period T  The time for one revolution (time to go around once), usually in seconds. Frequency f  the number of revolutions per second.  T = (1/f)

Particle moving in uniform circular motion, radius r (speed v = constant) Circumference = distance around= 2πr  Speed: v = (2πr/T) = 2πrf  Centripetal acceleration: a c = (v 2 /r) = (4 π 2 r/T 2 )

Example: Centripetal Acceleration of the Earth Problem 1: Calculate the centripetal acceleration of the Earth as it moves in its orbit around the Sun. NOTE: The radius of the Earth's orbit (from a table) is r ~ 1.5  m Problem 2: Calculate the centripetal acceleration due to the rotation of the Earth relative to the poles & compare with geo-stationary satellites. NOTE: From a table, the radius of the Earth is r ~ 6.4  10 6 m & the height of geo-stationary satellites is ~ 3.6  10 7 m

Tangential & Radial Acceleration Consider an object moving in a curved path. If the speed |v| of object is changing, there is an acceleration in the direction of motion. ≡ Tangential Acceleration a t ≡ |dv/dt| But, there is also always a radial (or centripetal) acceleration perpendicular to the direction of motion. ≡ Radial (Centripetal) Acceleration a r = |a c| ≡ (v 2 /r)

Total Acceleration  In this case there are always two  vector components of the acceleration: Tangential: a t = |dv/dt| & Radial: a r = (v 2 /r) Total Acceleration is the vector sum: a = a R + a t

Tangential & Radial acceleration Example: Over the Rise Problem: A car undergoes a constant acceleration of a = 0.3 m/s 2 parallel to the roadway. It passes over a rise in the roadway such that the top of the rise is shaped like a circle of radius r = 515 m. At the moment it is at the top of the rise, its velocity vector v is horizontal & has a magnitude of v = 6.0 m/s. What is the direction of the total acceleration vector a for the car at this instant?