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Unformatted text preview: CHAPTER 9 Rotation 1* Two points are on a disk turning at constant angular velocity, one point on the rim and the other halfway between the rim and the axis. Which point moves the greater distance in a given time? Which turns through the greater angle? Which has the greater speed? The greater angular velocity? The greater tangential acceleration? The greater angular acceleration? The greater centripetal acceleration? 1. The point on the rim moves the greater distance. 2. Both turn through the same angle. 3. The point on the rim has the greater speed 4. Both have the same angular velocity. 5. Both have zero tangential acceleration. 6. Both have zero angular acceleration. 7. The point on the rim has the greater centripetal acceleration. 2 True or false: ( a ) Angular velocity and linear velocity have the same dimensions. ( b ) All parts of a rotating wheel must have the same angular velocity. ( c ) All parts of a rotating wheel must have the same angular acceleration. ( a ) False ( b ) True ( c ) True 3 Starting from rest, a disk takes 10 revolutions to reach an angular velocity w . At constant angular acceleration, how many additional revolutions are required to reach an angular velocity of 2 w ? ( a ) 10 rev ( b ) 20 rev ( c ) 30 rev ( d ) 40 rev ( e ) 50 rev. From Equ. 9-9; w 2 q q 2 = 4 q 1 ; q = 3 q 1 = 30 rev; ( c ) 4 A particle moves in a circle of radius 90 m with a constant speed of 25 m/s. ( a ) What is its angular velocity in radians per second about the center of the circle? ( b ) How many revolutions does it make in 30 s? ( a ) w = v / r ( b ) q = w t w = (25/90) rad/s = 0.278 rad/s q = 8.33 rad = 1.33 rev. 5* A wheel starts from rest with constant angular acceleration of 2.6 rad/s 2 . After 6 s, ( a ) What is its angular velocity? ( b ) Through what angle has the wheel turned? ( c ) How many revolutions has it made? ( d ) What is the speed and acceleration of a point 0.3 m from the axis of rotation? ( a ) w = a t ( b ), ( c ) q = 1/2 a t 2 ( d ) v = w r , a c = r w 2 , a t = r a ; a = ( a t 2 + a c 2 ) 1/2 w = (2.6 6) rad/s = 15.6 rad/s q = 46.8 rad = 7.45 rev v = (15.6 0.3) m/s = 4.68 m/s; a =[(0.3 15.6 2 ) 2 + (0.3 2.6) 2 ] 1/2 m/s 2 = 73 m/s 2 Chapter 9 Rotation 6 When a turntable rotating at 33 1/3 rev/min is shut off, it comes to rest in 26 s. Assuming constant angular acceler- ation, find ( a ) the angular acceleration, ( b ) the average angular velocity of the turntable, and ( c ) the number of re- volutions it makes before stopping. ( a ) a = w / t ( b ) w av = 1/2 w ( c ) q = w av t a = (33.3 2 p /60 26) rad/s 2 = 0.134 rad/s 2 w av = 1/2(33.3 2 p /60) rad/s = 1.75 rad/s q = (1.75 26) rad = 45.4 rad = 7.22 rev 7 A disk of radius 12 cm, initially at rest, begins rotating about its axis with a constant angular acceleration of 8 rad/s 2 . At t = 5 s, what are ( a ) the angular velocity of the disk, and ( b ) the tangential acceleration a t and the centripetal acceleration...
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- Spring '08