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 displacement at

angular displacement of 3 radian.

Answer 1

$w² = w_0² +2\alpha \theta$

$a. \ 8² = w_0² + 2\alpha (0)\\ \quad64 = w_0² + 0\\ \quad w_0 = 8\ rad/s$

$0² = w_0² + 2\alpha(4)\\ 0 = 8² + 8\alpha\\ \alpha = \dfrac{-64}{8} = -8\ rad/s²$

b. $w² = 8² + 2(-8)(3)\\$

$\quad w² = 64 -48\\ \quad w= \sqrt{16} = 4\ rad/s$