How is rotational motion related to linear motion? HW:

Angular Acceleration How did we determine angular velocity? We simply applied the linear velocity equation in terms of radians! So what is angular acceleration? Symbol: α Units: rad/sec2 Look familiar?

Tying together relationships What expression related angular displacement to displacement and angular velocity to velocity? Change l to s How is each relationship similar? So, what do you think is the equation that relates angular and linear acceleration?

How do all the kinematic equations relate to rotational motion? Kinematics Rotational

Making things even easier! A lot of the time, rotational questions give you the angular velocity as “rpm” or “rps”. We can convert this since one rotation is 2π radians! What is 5.5 rps in rad/s? “rps” is simply frequency, so this conversion can be written as:

White Board Activity A centrifuge rotor is accelerated from rest to 20,000 rpm in 30 s. What is the average angular acceleration? b. Through how many revolutions has the centrifuge rotor turned during its acceleration period, assuming constant angular acceleration?

Solutions ωi = 0, so that leaves just ωf ωf=2πf = 2π rad/rev x 333.3 rev/s ωf ≈ 2100 rad/s α = 70 rad/sec2 b. Recall one revolution is 2π radians. θ = 0 + .5(70 rad/s2)(30s)2 θ = 3.15 x 104 rad 5000 rev

Summary How is linear acceleration, velocity and displacement related to it’s rotational counterpart? How is frequency related to angular velocity? What is “rps” and “rpm” stand for? What do both represent? l=rθ, v = rω, a = rα ω = 2πf Revolutions per minute and revolutions per second. This is frequency (Hz)