Question

The angular acceleration of an rotating body is define by the relation 𝔞 = - kθ. Determine a) the value of k if angular velocity is 8 rad/sec at angular displacement of 0 radian and angular velocity is 0 rad/sec at angular displacement of 4 radian. B) find the angular velocity at angular displacement of 3 radian.

Answer 1

a) $\alpha =-k\theta$

$w² = w_0² +2\alpha s$

$w_0² = 8\ rad/s$

$0² = 8² +2\alpha(4)\\ \alpha = -8 rad/s²$

$-8= -k(0) \quad --(i)\\ -8 = -k(4) \quad --(ii)\\$

$\therefore k = 2\ s^{-2}$

b) $w² = w_0² +2\alpha s$

$w²=8²+2(-8)(3)\\ w² = 64 - 48\\ w² = 16\\ w= 4\ rads^{-1}$