2-Dimensional Motion IV Measuring Rotational Motion 7.1

Rotational Motion This is the motion of an object that is moving in a circle. The displacement cannot be found simply by using the shortest distance between two points. Instead we must use the arc length during the time travelled The angles will be measured in radians http://dept.physics.upenn.edu/courses/gladney/phys150/lectures/lecture_nov_03_1999.html

θ, π, and ° s = length of the arc r = radius θ = angle in radians θ = s/r = 2 πr/r = 2 π(rad) θ(rad) = π θ(deg) 180° Δθ = Δs r

While riding on a carousel that is rotating clockwise, a child travels through an arc length of 11.5 m. If the carousel has a diameter of 8.00 m, through what angular displacement does the child travel? Convert this angular displacement to degrees. Problem 7A pg 246

Angular Speed ω = angular speed ω = Δθ Δt A child at an ice cream parlor spins on a stool. If a child turns counter-clockwise through 10.0πrad during a 10.0 s interval, what is the average angular speed of the child’s feet. Problem 7B pg 248

Angular Acceleration α = angular acceleration α = ω2 – ω1 = Δω t2 – t1 Δt A car’s tire rotates at an initial angular speed of 21.5 rad/s. The driver accelerates, and after 3.5 s the tire’s angular speed is 28.0 rad/s. What is the tire’s average angular acceleration during the 3.5 s time interval? Problem 7C pg 249

Comparing Angular and Linear Quantities Rotational motion with constant angular acceleration Linear motion with constant acceleration ωf = ωi + αΔt vf = vi + aΔt Δθ = ωiΔt + ½ α(Δt)2 Δx = viΔt + ½ a(Δt)2 ωf2 = ωi2 + 2α(Δθ) vf2 = vi2 + 2a(Δx) Linear Angular x θ v ω a α

The wheel on an upside-down bicycle rotates with a constant angular acceleration of 3.5 rad/s2. If the initial angular speed of the wheel is 2.0 rad/s, through what angular displacement does the wheel rotate in 2.0 s? Problem 7D pg 251

Homework!!! Practice Problems 7A-7D the odds for each section