Rotational Motion and the Law of Gravity

 = angle from 0 r = radius of circle s = arc length (in radians)  = (in radians)

If you go all of the way around the circle, so for s = 360° = 2  r, so  =  (rad) =  (°) = 2  rad

Angular Displacement  angular displacement (rad) = change in arc length radius

If an ant is crawling around the lip of a coffee cup that is 15 cm wide, and walks for 3 cm, what is its angular displacement in radians and degrees? r = 15 cm/2 = 7.5 cm  s = 3 cm =.4 rad = 22.9°

Angular Speed Just like linear speed is displacement over time v =  x/  t Average angular speed is angular displacement over time  avg =  t  avg is “omega average”

My Mustang has 19” rims. If the tire spins with an angular speed of 45 rad/s, and you time it for 7 s, How many times did it spin?  avg =  t  avg = 45rad/s  t = 7 s  =  avg  t = 45 rad/s (7s) = 315 rad One spin = 2  rad 315 rad/2  = 50 spins

Angular Acceleration Just like linear acceleration is velocity / time a =  v/  t Angular acceleration is angular speed / time  =  t  = “alpha”

Tangential Speed =  t, ,  a b Which point is moving faster, a or b? v t = r  a t = r 

If time is kept small, tangential speed and acceleration are tangent to the radius vtvt atat

Centripetal Acceleration An object moving in a circle is accelerated toward the center

Forces that maintain circular motion Something moving in a circular path has a tendency to want to continue in a tangent path. A force must hold it in its circular path.

Universal Gravitation All matter creates a force of gravity with other matter

F g = mg

Find your mass (kg) (weight in lbs ÷ 2.2 kg/lb) Find “g” on Mars and your weight there, if Mars has a mass of x Kg and average radius of x 10 6 m. F g = m you (3.71m/s 2 ) x.455 lb/kg