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19 - Rotational Kinematics

# 19 - Rotational Kinematics - Angular velocity and...

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Angular velocity and acceleration For next time: Read: Serway 10.1 – 10.6 Homework: Handout, Problems 7, 9, & 11

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A natural measure of “angle” r R C = 2 π r C = 2 π R 2 π r = C r r = 2 π R 2 π R = C R = 2 π
s i r i 2 r i 2 s i

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s i 2 s i 3 s i r i 3 r i
s i r i 4 r i 2 s i 3 s i 4 s i θ (in radians) s r θ=

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How many radians in 90 0 ? A) π B) π /2 C) 2 π D) 3/2 π
How many radians in 90 0 ? 00 90 90 1 = × 0 2 90 90 360 π 0 0 0 90 90 2 360 0 1 90 2 4 = × 2 =

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A box is fastened to a string that is wrapped around a pulley of radius 4 m. The pulley turns through an angle of 43 0 . What is the distance, d , that the box moves? d θ r = 4 m A) 1.5 m B) 2 m C) 2.5 m D) 3 m d
A box is fastened to a string that is wrapped around a pulley of radius 4 m. The pulley turns through an angle of .75 rad . What is the distance, d , that the box moves? d θ r = 4 m = s / r = d / r d = r d = 4m (0.75 rad) d = 3 m rad d = 3 m d

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Rigid-body rotation • Location of point P described in polar coordinates • Angle θ measured in radians x y P r s () 2 radians 360 π= ° 1 rad = 57.3 ° s r
Angular displacement x y P i

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19 - Rotational Kinematics - Angular velocity and...

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