a) Time taken =6.39 s
b) Angle of rotation while coming to rest = 188.17 rad
Explanation:
Initial angular velocity of the drum [tex]\omega_{0} = 19.8 rad/s^{2}[/tex]
Angular acceleration of the drum [tex]\alpha = -3.02 rad/s^{2}[/tex]
a.) We know that
[tex]\omega =\omega_{0} + \alpha t[/tex]
[tex]0 = 19.8 - 3.02 t[/tex]
[tex]t = \frac{19.8}{3.02}[/tex]
[tex]t = 6.39s[/tex]
b.) we know that
[tex]\theta = \omega_{0} t + \frac{1}{2} \alpha t^{2}[/tex]
[tex]\theta = 19.8 \times 6.39 + \frac{1}{2} \times 3.02 \times 6.39^{2}[/tex]
[tex]\theta =188.17 rad[/tex]
