Determine the angle.. rotation in physics.?

Question

What angle is passed through by a flywheel which changes its speed from 1200 rpm to 1800 rpm in 1/2 min?

Answer 1

Start by rewriting the angular speeds in rad/min; 1 rpm = 2π rad/min, so 1200 rpm = 2400π rad/min and 1800 rpm = 3600π rad/min. We'll call these angular velocities ω for the final angular velocity (3600π rad/min) and ω_0 for the initial angular velocity (2400π rad/min). Then calculate the angular acceleration, which is just α = (ω - ω_0) / t, where t = 0.5 min is the elapsed time. You should get 2400π rad/min^2. Now simply use the equation ω^2 = (ω_0)^2 + 2αθ, which is the rotational analogue to v^2 = (v_0)^2 + 2ax from linear motion. You were given ω and ω_0, and you have calculated α, so your only unknown is the angle θ, and you can now solve for it.