Question

7) A disk is initially spinning about its center at 18 rad/s counter-clockwise and a constant angular acceleration of 2.9 rad/s2 is applied to it clockwise. How many revolutions does it make before it stops?

Answer 1

w_o = 18 rad/s ( initial angular velocity)

= - 2.9 rad/s² ( angular acceleration clockwise)

before it stops means w_f ( final angular velocity) = 0 rad/sec

using rotational kinematics, we have

w_f² - w_o² = 2

0² - 18² = 2 ( - 2.9)

= 55.86 radians

so,

number of revolutions = 55.86 / 2

number of revolutions = 8.89 revs ( usually, number of revolutions is given as an integer)