Answer to Question #216680 in Mechanics | Relativity for Vishal nath

Question

a machine part rotates at an angular speed of wi. its speed is then increased at wf at an angular acceleration of a. if both the inital and final angular sppeed are now doubled and the anglure accleration remains the smae , by what factor is the angluar displacement changed?

Answer 1

$\omega_f^2=\omega_i^2+2\alpha\theta\\ \theta=\frac{\omega_f^2-\omega_i^2}{2\alpha}\\ \theta_n=\frac{(2\omega_f)^2-(2\omega_i)^2}{2\alpha}\\ \theta_n=4\dfrac{(\omega_f)^2-(\omega_i)^2}{2\alpha}\\ \theta_n=4\theta$

The angular displacement changed by a factor of 4