Rotational Motion and the Law of Gravity

Rotational Motion and the Law of Gravity

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

If you go all of the way around the circle, so for s = 360° = 2pr, so q = = 2p rad q (rad) = q (°)

Angular Displacement Dq = 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 cmDs = 3 cm = .4 rad = 22.9°

Angular Speed Just like linear speed is displacement over time v = Dx/Dt Average angular speed is angular displacement over time wavg = Dq/Dt wavg 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? wavg = Dq/Dt wavg = 45rad/s Dt = 7 s Dq = wavgDt = 45 rad/s (7s) = 315 rad One spin = 2p rad 315 rad/2p = 50 spins

Angular Acceleration • Just like linear acceleration is velocity / time • a = Dv/Dt • Angular acceleration is angular speed / time • = Dw/Dt • a = “alpha”

Tangential Speed a b = Dt, Dq, w Which point is moving faster, a or b? vt = rw at = ra

If time is kept small, tangential speed and acceleration are tangent to the radius vt at

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

Fg = mg

Find your mass (kg) (weight in lbs ÷ 2.2 lb/kg) Find “g” on Mars and your weight there, if Mars has a mass of 6.424 x 1023Kg and average radius of 3.398 x 106 m. Fg = myou(3.71m/s2) x .455 lb/kg

Rotational Motion and the Law of Gravity