General Physics 1
(Phys 110 : Mechanics)
CHAPTER 4
Motion in 2D and 3D
Phys 110
1. Position vector (π):
Chapter 4 : Motion in 2D and 3D
Revision :
Lesson 5 of 5 Slide 1
π π = π π π + π π π + π(π)π
Particleβs motion in
2D
Position vector 1
Position vector 2
2. Displacement vector (βπ):
Phys 110
3. Average Velocity (ππππ):
Chapter 4 : Motion in 2D and 3D
Revision :
Lesson 5 of 5 Slide 2
4. Instantaneous Velocity (Velocity) (π):
direction of ππππ = direction of βπ
direction of π : along the tangent to path
Phys 110
5. Average Acceleration (ππππ):
Chapter 4 : Motion in 2D and 3D
Revision :
Lesson 5 of 5 Slide 3
6. Instantaneous Acceleration (Acceleration) (π):
direction of π : not related to path
Phys 110
The horizontal Range:
The maximum height:
Chapter 4 : Motion in 2D and 3D
Revision :
Lesson 5 of 5 Slide 4
The Equation of path:
Vertical Motion (y-axis)
Horizontal Motion (x-axis)
Substitute:
π β π
π β ππ β (βπ) ππ β πππ β ππππππ½π
π β ππ π£π₯ = π£ππ₯ π₯ β π₯π = π£ππ₯π‘ π£ππ₯ = π£ππππ ππ
7. Projectile Motion:
Phys 110
1. to define the uniform circular motion.
2. to identify the particle's velocity in the uniform circular motion.
3. to define the centripetal acceleration in magnitude and direction for a particle in uniform circular motion.
4. to calculate the time of revolution (period) for a particle in uniform circular motion.
5. to calculate the distance that the particle travels during one period in circular motion.
6. to determine the velocity and acceleration vectors in a
circular path in which the center at the origin of xy-plane.
Chapter 4 : Motion in 2D and 3D
Objectives covered in this lesson :
Lesson 5 of 5 Slide 5
Motion in 2D and 3D:
Uniform Circular Motion
Phys 110
Lesson 5 of 5 Slide 6
Chapter 4 : Motion in 2D and 3D
4-7 Uniform Circular Motion :
Circumference of circle = 2ππ
Period: is the time for a particle to go around a closed path exactly once.
In this motion:
Velocityβs:
magnitude (speed) = constant (does not change).
direction: changes but is always tangent to the circle in the direction of motion.
Accelerationβs:
magnitude = constant (but not zero).
direction: changes but is always directed towards the center of the circle.
centripetal acceleration = always directed radially inwards.
Phys 110
Lesson 5 of 5 Slide 7
Chapter 4 : Motion in 2D and 3D
4-7 Uniform Circular Motion :
Phys 110
Lesson 5 of 5 Slide 8
Chapter 4 : Motion in 2D and 3D
Answer: (a) β4 m/s π , (b) β8 m/π 2 π
4-7 Uniform Circular Motion :
Phys 110
Lesson 5 of 5 Slide 9
Chapter 4 : Motion in 2D and 3D
Sample Problem (4-10) :
Phys 110
Lesson 5 of 5 Slide 10
Chapter 4 : Motion in 2D and 3D
Sample Problem (4-10) :
Motion in 2D and 3D:
Uniform Circular Motion.
Phys 110
Lesson 5 of 5 Slide 11 (last)
Summary:
Any Questions?
Next lesson we will start Chapter 5 and will cover:
Section (5-1).
Section (5-2).
Section (5-3).
Section (5-4) without the βinertial reference framesβ.
Section (5-5).
Section (5-6).
Chapter 4 : Motion in 2D and 3D
