Holt Physics Chapter 7: Rotational Motion and the Law of Gravity I. Section 7-1: Measuring Rotational Motion
A. When something spins it undergoes “rotational motion”. When something spins around a single point it is called “circular motion”. B. We measure how fast something spins not in m/s (different points on the object are spinning at different velocities) but by measuring the angle described in a given time period. C. Angles can be measured in radians (rad)
1. The radian is the ratio of the arc length (s) to the radius (r) of a circle
(insert fig. 7-1 here)
2. The radian is a “pure number” with no units (the abbreviation “rad” is always used) 3. Conversions:
360o = 2π rad
360o = 6.28 rad
Θ(rad) = π/180o Θ(deg)
Θ(rad) = .0174533 Θ(deg)
(insert fig. 7-3)
D. Angular displacement describes how much an object has rotated relative to a reference line
(insert fig 7-4)
ΔΘ = Δs/r
angular displacement = change in arc length/radius
E. Watch your sign! Θ is considered positive when rotating COUNTERclockwise (when viewed from above). Therefore an angle of ½π rad = -1½π rad F. Angular Speed (ω = “omega”) describes the rate of rotation. Average angular speed is measured in radians per second.
ωavg = ΔΘ/Δt
average angular speed = angular displacement/time
G. Angular Acceleration (α = “alpha”) occurs when angular speed changes. Remember acceleration? a = velocity/time ??
αavg = ω2 – ω1/t2 – t1 = Δω/Δt
average angular acceleration = change in speed/time
H. “All points on a rotating rigid object have the same angular acceleration and angular speed.” P.250 II. Section 7-2: Tangential and...