Download Section 8-2 Center of Mass

Unit 6 Notes: Part 1 – Corresponds to Chapter 7 text - Chapter 7 Rotational Motion / Gravitation
1. Rotational Motion – motion of a body that spins about an axis
a. Axis of rotation – line about which rotation occurs
i. Perpendicular to motion
ii. Through center of motion
b. Linear equations will not work b/c direction of rotational motion is constantly
changing.
2. Analyzing circular motion
a. describe through angles of motion
b. all points on rotating body move through same angle
c. set up a fixed reference line
i. r = distance from center
ii. Θ = angle from reference line
iii. s = arc length – distance moved along the circumference of circle.
3. Measuring Angles
a. Use radians – angle whose arc length (s) is equal to the radius (r)
Θ=s
r
i. Pure number therefore, use (rad) as label
ii. 1 revolution (s) = 2πr
iii. One complete revolution = 360o
Θ = s = 2πr = 2 π rad
r
r
b. To convert angle in degrees to radians
i. Θ (rad) = π
Θ (deg.)
o
180
4. Angular Displacement – angle through which a point, line, or body is rotated in a specific
direction and about a specific axis.
a. ∆Θ (rad) = ∆s
r
i. (+) ∆s = counterclockwise rotation
ii. (-) ∆s = clockwise rotation
5. Angular Speed – rate that a body rotates around an axis
a. ω = greek letter omega
b. ωavg = ∆Θ (rad)
∆t
c. SI = rad / s
d. 1 revolution = 2π rad
6. Angular Acceleration – rate of change of ω
a. α = Greek letter alpha
b. αavg = ω2 – ω1 = ∆ω
or (a/d) → tangential acceleration (m/s2) / distance (m)
t2 – t1
∆t
2
c. SI = rad/s
d. All points on a rigid body have the same ω and α
1
7. Tangential Speed – aka – instantaneous linear speed of a point along a circular path.
a. vt
b. vt = r ω
c. SI = m/s
d. See Figure 7.4 on pg. 189
e. Linear speed of a point on the rotating object increases with as the object’s distance
from the center (r) increases.
f. Although every point on the rotating object has the same angular speed (ω), not
every point has the same linear (tangential) speed.
8. Centripetal Acceleration – acceleration directed toward the center of a circular path
a. Ex. Although a car moves at a constant speed of 40 km/h around a curve, it still has
an acceleration because the direction of the velocity changes.
b. ac
c.
or
2
d. SI = m/s
9. Newton’s Law of Gravitation
a. Gravitational Force – attractive force between two objects
i. Increased mass = increased Fg
ii. Increased distance between = decreased Fg
iii. Fg = G (m1)(m2)
r2
iv. G =Constant of Universal Gravitation = 6.67 x 10-11 N • m2
kg2
b. Calculate Fg of an object on the surface of a spherical object
i. Fg = G (ME)(m2)
(RE)2
*Remember Fg = (m) (g)
2