1. Rotational Motion
and the
Law of Gravity

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

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

5. Angular Displacement Dq =
angular displacement (rad) = change in arc length
radius

6. 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 Ds = 3 cm
= .4 rad
= 22.9°

8. 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”

9. 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 rad/2p = 50 spins

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

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

12. If time is kept small, tangential speed and acceleration are tangent to the radiusvt at

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

14. 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.

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

16. Fg = mg

17. 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 x 1023Kg and average radius of x 106 m.
Fg = myou(3.71m/s2) x .455 lb/kg