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
