Notes

1.2 – Math Review

Cross Product • Cross (vector) product of two vectors gives you a vector perpendicular to both whose magnitude is equal to the area of a parallelogram defined by the two initial vectors • Positive direction of the cross product is given by the right-hand rule • Cross product of parallel vectors is zero. Calculating the Cross Product • |A ⃗×B ⃗ |=AB sin⁡θ • A ⃗×B ⃗=|■8(i ̂&j ̂&k ̂@A_x&A_y&A_z@B_x&B_y&B_z )|=(A_y B_z−A_z B_y ) i ̂+(A_z B_x−A_x B_z ) j ̂+(A_x B_y−A_y B_x ) k ̂ Cross Product Properties • A ⃗×B ⃗=−B ⃗×A ⃗ • A ⃗×(B ⃗+C ⃗ )=A ⃗×B ⃗+A ⃗×C ⃗ • c(A ⃗×B ⃗ )=(cA ⃗ )×B ⃗=A ⃗×(cB ⃗ ) • d/dt (A ⃗×B ⃗ )=(dA ⃗)/dt×B ⃗+A ⃗×(dB ⃗)/dt Unites

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2.1 – Describing Motion I

Position / Displacement • An object

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2.2 – Describing Motion II

Special Case: Constant Acceleration • For cases of constant acceleration, we can derive a set of "kinematic equations" that will allow us to solve for unknown quantities Deriving the Kinematic Equations Free Fall • When the only force acting on an object is the force of gravity, we refer to object

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2.3 – Projectile Motion

What Is a Projectile • A projectile is an object that is in acted upon only by gravity • In reality, air resistance plays a role • Typically, projectiles are objects launched at an angle Path of a Projectile • Projectiles launched at an angle move in parabolic arcs Independence of Motion • Projectiles launched at an angle have motion in two dimensions ○ Vertical - like free fall ○ Horizontal - 0 acceleration • Vertical motion and horizontal motion can be treated separately! Angled Projectiles • For objects launched at an angle, you must first break up the object

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2.4 – Circular & Relative Motion

Radians and Degrees • In degrees, once around a circle is 360° • In radians, once around a circle is 2π • A radian measures a distance around an arc equal to the length of the arcs radius • Δs=C=2πr Linear vs. Angular Displacement • Linear position / displacement given by Δr or Δs • Angular position / displacement given by Δθ • s=rθ • Δs=rΔθ Linear vs. Angular Velocity • Linear speed / velocity given by v ⃗ • Angular speed / velocity given by ω ⃗ • v ⃗=(ds ⃗)/dt • ω ⃗=(dθ ⃗)/dt Direction of Angular Velocity Converting Linear to Angular Velocity Linear vs. Angular Acceleration • Linear acceleration is given by a ⃗ • Angular acceleration is given by α ⃗ • a ⃗=(dv ⃗)/dt • α ⃗=(dω ⃗)/dt Centripetal Acceleration Reference Frames • A reference frame describes the motion of an observer ○ Most common reference frame is Earth • Laws of physics we study in this course assume were in an inertial, non-accelerating reference frame • There is no way to distinguish between motion at rest and motion at a constant velocity in an inertial reference frame Calculating Relative Velocities • Consider two objects, A and B. • Calculating the velocity of A with respect of reference frame B (and vice versa) is straightforward • Example: ○ Speed of car with respect to the ground ○ Walking on a train, speed of a person with respect to the train • v_(A with respect to C)=v_(A with respect to B)+v_(B with respect to C) Linear vs. Angular

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