angular position standard unit: radians
angular position must be in radians
Angular Displacement Convention: positive is counterclockwise must be in radians
Angular velocity Average angular velocity (Instantaneous) angular velocity Unit: radian per second (rad/s)
Angular acceleration Average angular acceleration (Instantaneous) angular acceleration Unit: radian per second squared (rad/s2)
Angular velocity and angular acceleration are vectors; they have directions. direction: Right-hand rule direction: speeding up or slowing down
anddirections direction: Right-hand rule direction: speeding up or slowing down
Rotational kinematics Valid only when is constant
Linear & rotational variables must be in radians
grindstone A grindstone rotates at constant angular acceleration of 0.35 rad/s2. At time t = 0, it has an angular velocity of – 4.6 rad/s and a radial line on it is horizontal, at the angular position θ0 = 0. • At what time is the radial line at angular position θ = 5.0 rev? • At what time t does the grindstone momentarily stop?
rotor While you are operating a Rotor (a large, vertical, rotating cylinder found in amusement parks), you spot a passenger in acute distress and decrease the angular velocity of the cylinder from 3.40 rad/s to 2.00 rad/s in 20.0 rev, at constant angular acceleration. (a) What is the angular acceleration during this decrease in angular speed? (b) How much time did the speed decrease take? –0301 rad/s2 46.5 s
cd In a typical CD player, the constant tangential speed of the surface at the point of the laser–lens system is 1.3 m/s. (a) Find the angular speed of the disc in revolutions per minute when information is being read from the innermost first track(r = 23 mm) and the outermost final track (r = 58 mm). (b) The maximum playing time of a standard music disc is 74 min and 33 s. How many revolutions does the disc make during that time? (c) What is the angular acceleration of the compact disc over the 4,473-s time interval? 2.1 × 102 rev/min 2.8 × 104 rev –7.6 × 10–3rad/s2
turntable The angular velocity of a rotating turntable is given in rad/s by . Assume that at t = 0, θ = 0. • What is the angular position, angular velocity and angular acceleration at s? • What is its average angular velocity and acceleration between s and s?