Two-Dimensional Kinematics: Solving Problems for Objects Moving in a Plane, Slides of Physics

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Chapter Goal: To learn how to solve problems for objects that move in a plane. Slide 4-

Chapter 4- Kinematics in 2 Dimensions

Two Dimensions- Kinematics Objectives

• (^) Student Learning Objectives  (^) To identify the acceleration vector for curvilinear motion.  (^) To compute two-dimensional trajectories.  (^) To understand projectile motion.  (^) To understand relative motion.  (^) To understand the kinematics of uniform circular motion.  (^) To understand angular acceleration and the kinematics of non-uniform circular motion. 2

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Two Dimensional Kinematics

• (^) Displacement in two Dimensional motion. Δ 𝑟 ⃗ = 𝑟 ⃗ 2 − 𝑟 ⃗ 1 =¿

4.1 Average Velocity in 2- D

Average velocity is: 5 Direction of average velocity is the direction of -----------.

• (^) If the velocity vector’s angle is measured from the positive -direction, the velocity components are: Slide 4- where the particle’s speed is  (^) Conversely, if we know the velocity components, we can determine the direction of motion:

Components of velocity

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Two Different Uses of the tangent lines

• (^) Avoid confusion and pitfalls!

4.1 Motion in Two Dimensions Ch 4- 10

Acceleration- graphically:

• (^) Object here is changing direction without speeding up or slowing down, but at constant speed.
• (^) How can we tell that the speed is constant?
• (^) Acceleration vectors are pointing towards the center of motion 11

• (^) An object’s acceleration can be decomposed into components parallel and perpendicular to the velocity.
• (^) is the piece of the acceleration that causes the ---------.
• (^) is the piece of the acceleration that causes the object to change ?.
• (^) An object changing direction always has a component of acceleration? to the direction of motion.

Analyzing the Acceleration Vector

Slide 4- 13

Two-Dimensional Acceleration Graphically

Slide 4- Components of acceleration. changes ------- ; changes ---------.

Acceleration- components summary- how

they affect velocity

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3. A fish swimming in a horizontal plane has velocity = (4.00 + 1.00 ) m/s at a point in the ocean where the position relative to a certain rock is (10.00 – 4.00 ) m. After the fish swims with constant acceleration for 20.0 s, its velocity is (20.00 – 5.00 ) m/s. (a) What are the components of the acceleration? (b) What is the direction of the acceleration with respect to unit vector?

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4.2 Projectile Motion

• (^) Special case of two D motion: When the acceleration is ----- in horizontal direction and when acceleration in the vertical direction is ----, we call this motion a projectile motion.
• (^) Objects that move in --- dimensions under the influence of -------- -------- and ----- ----- -------to power their motion are called ----------
• (^) Their path,- trajectory, as observed by a ---------- observer is a ------------
• (^) At any given instant of time, the object’s velocity ------- ------ to the horizontal is constant
• (^) At any instant, the ---------- -------- ------------is changing due to ------ due to ---------

Projectile

20 For Motion in For Motion in