Ch 01: Units & VectorsSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Vectors vs. Scalars

Concept #2: Combining Vectors

Concept #3: Decomposing Vectors

Concept #4: Combining Vectors (Practice Intro)

Practice: You walk 3 m down, then 4 m to the right. Draw your displacement and calculate its magnitude and direction.

Practice: You walk 7 m down, then 10 m directed at 53 degrees below the positive x axis. Draw your displacement and calculate its magnitude and direction.

Practice: Three forces act on an object: A = 2 N @ 0 degrees, B = 7 N @ -90 degrees, and C N = 5 @ -37 degrees. Calculate the magnitude and direction of the NET force acting on the object.

Additional Problems
A hiker on a trek needs to cross some rough terrain. In order to do so, she has to walk east for half a mile, then head 30o north of east for a quarter mile, then finally she can reach her destination by heading due west for a mile. Because of the indirect path she had to take to reach her final destination, she traveled a pretty far distance. But how far did she actually get from her starting point, as the crow flies?
A vector A has a magnitude of 10, and points in a direction of 50° counter-clockwise from the x-axis. A vector B has a magnitude of 8, and points in a direction of 45° clockwise from the x-axis. What is the magnitude of A + B?  
A vector A has a magnitude of 10, and points in a direction of 50° counter-clockwise from the x-axis. A vector B has a magnitude of 8, and points in a direction of 45° clockwise from the x-axis. What is the direction of A + B?
A vector A has a magnitude of 5, and points in a direction of 50° counter-clockwise from the y-axis. A vector B has a magnitude of 7, and points in a direction of 30° clockwise from the x-axis. What is the magnitude of A - B?
A vector A has a magnitude of 5, and points in a direction of 50° counter-clockwise from the y-axis. A vector B has a magnitude of 7, and points in a direction of 30° clockwise from the x-axis. What is the direction of A - B?
A vector A has a magnitude of 5 and makes an angle of 30° clockwise from the negative x-axis. What are the components of the vector -A, using the appropriate signs to denote whether the vector points along the positive or negative axis. 
A vector A has a magnitude of 4, and points in a direction of 40° counter-clockwise from the negative x-axis. A vector B has a magnitude of 4.5, and points in a direction of 30° clockwise from the x-axis. What is the magnitude of the vector 2A – 3B?
An object moves 8.0 m north and then 5.0 m south. Find both the distance traveled and the magnitude of the displacement vector. A) 3.0 m, 13.0 m B) 3.0 m, 3.0 m C) 13.0 m, 13.0 m D) 13.0 m, 3.0 m
Given the vectors in the following graph, write  (A - B) + C in vector notation ( i.e  a = axî + ayĵ) 
Consider the following diagram. Which of the following pairs of statements is true? Ia. A − B = C Ib. A − D = C Ic. A − C = B Id. B − A = C IIa. A = D − C IIb. A = D − B   1. Ia, IIb 2. Ic, IIb 3. Id, IIa 4. Id, IIb 5. Ib, IIb 6. Ib, IIa 7. Ic, IIa 8. Ia, IIa
If two vectors have magnitudes A and B, with A ≥ B, and their vector sum has magnitude C, which relation below must be true?a) C ≥ A - Bb) C = A + Bc) C ≥ Bd) C ≠ 0
A vector A has a magnitude of 4, and points in a direction of 40° counter-clockwise from the negative x-axis. A vector B has a magnitude of 4.5, and points in a direction of 30° clockwise from the x-axis. What is the direction of the vector 2A – 3B?
Find the magnitude and direction of the resultant R of the three vectors shown in the figure. The vectors have the following magnitudes; A = 7.9, B = 5.0, and C = 8.0. Express the direction of the vector sum by specifying the angle it makes with the positive x-axis with the counterclockwise angles taken to be positive.