October 29 - Rotation Solutions

# October 29 - Rotation Solutions - 9.3 t2 dz Writing Eq(2.16...

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9.3. IDENTIFY: () z z d t dt . Writing Eq.(2.16) in terms of angular quantities gives 2 1 t z t dt  . SET UP: 1 nn d t nt dt and 1 1 1 t dt t n EXECUTE: (a) A must have units of rad/s and B must have units of 3 rad/s . (b) 3 ( ) 2 (3.00 rad/s ) z t Bt t  . (i) For 0 t , 0 z . (ii) For 5.00 s t , 2 15.0 rad/s z . (c) 2 1 2 3 3 1 2 1 2 1 2 1 3 ( ) ( ) ( ) t t A Bt dt A t t B t t  . For 1 0 t and 2 2.00 s t , 33 1 21 3 (2.75 rad/s)(2.00 s) (1.50 rad/s )(2.00 s) 9.50 rad . EVALUATE: Both z and z are positive and the angular speed is increasing. 9.16. IDENTIFY: Use the constant angular acceleration equations, applied to the first revolution and to the first two revolutions. SET UP: Let the direction the disk is rotating be positive. 1 rev 2 rad . Let t be the time for the first revolution. The time for the first two revolutions is 0.750 s t . EXECUTE: (a) 2 1 00 2 zz tt applied to the first and to the first two revolutions gives 2 1 2 z t  and 2 1 2

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October 29 - Rotation Solutions - 9.3 t2 dz Writing Eq(2.16...

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