How many revolutions does the wheel turn through during this time interval?

Question

A wheel rotates about a fixed axis with an initial angular velocity of 48 rad/s. During a 7 s interval, the angular velocity increases to 120 rad/s. Assume the angular acceleration was constant during this time interval. How many revolutions does the wheel turn through this time interval?

Answer 1

Since the angular acceleration is constant, you can take the average of 48 and 120 = 83 rads/sec.

Thus 7*83=581 revs.

Answer 2

a million ) form of revolutions=angular displacement / 2 pi angular displacement= straightforward angular speed* time angular displacement=(very final ang.vel.+preliminary ang vel)*time/2 =(70 + 31)*9 / 2 = 454.5 radian form of revolutions=454.5 / 2 pi= seventy two.34 2)preliminary ang vel=106*2 pi / 60= 11.a million radian/2d very final vel= 0 Angular acceleration=2.86 rad/s^2 time=replace in ang. vel. / ang. acc.=11.a million / 2.86=3.881 s attitude=straightforward ang vel. * time=5.fifty 5*3.88=21.fifty 3 radian