Question # 2 The flywheel of a prototype car engine is under test. The angular p

Question

Question # 2
The flywheel of a prototype car engine is under test. The angular position ? of the flywheel is given by ? = (3.0rad/s3)t3 and the diameter of the flywheel is 36cm.

(a)Find the distance that a particle on the rim moves during that time interval.
(b) Find the angle ?, in radians and in degree, at times t1 = 3.0s and t2 = 6.0s.
(c) Find the average angular velocity, in rad/s and in rev/min, between t1 = 3s and t2 = 6s.
(d) Find the instantaneous angular velocity at time t1 = 3.0s and t2 = 6.0s.

Explanation / Answer

given that ? = ( 3.0 rad/s3)t3 diameter of the fly wheel d = 0.36 m b) at times t1 = 3.0s and t2 = 6.0s ?1 = ( 3.0 rad/s3)(3.0 s)3 = 81 rad ( 3600/ 2p rad) = 4643.310 ?2 = ( 3.0 rad/s3)(6.0 s)3 = 648 rad ( 3600/ 2p rad) = 37146.490 a)?? = ?2 -?1 = 567 rad radius of wheel = diamter /2 = 0.36 m/2 = 0.18 s = r?? =102.06 m c) average angular velocity ?(avg) = ?2 -?1/t2 - t1 =567 rad/3 s = 189 rad /s = 189 rad/s ( 1 rev/ 2p rad ) ( 60s/ 1 min) =1805.73 rev/min d)? = d?/dt = d/dt (( 3.0 rad/s3)t3) = ( 3.0 rad/s^3) 3 t^2 = (9 rad/s^3) t^2 at time t = 3.0 s = ( 9.0 rad/s^3) ( 3.0s)2 = 81 rad/s at time t = 6.0 s = ( 9.0 rad/s^3) ( 6.0s)2 = 324 rad/s

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