I've been tasked with calculating the HP required to spin a turntable from rest to a desired RPM. I've tried calculating this out using two different methods, and have came upon two different solutions. I've went through my formulas multiple times but have not found why I am getting two different answers (one is double of the other). Variables: r = radius of turntable [m] m = mass of turntable [kg] ω = desired angular speed [RPM]; converted to rad/s using 2*pi/60. t = desired time Method 1: Energy Erot = 1/2 * I * ω^2 This gives me my energy required in Joules which I then divide by the time to get my required power. Using the moment of inertia of a think disc (1/2*m*r^2), my final equation looks like this: P = [(1/2)*(1/2)(mr^2)*ω^2]/t = [(1/4)*(mr^2)*ω^2]/t Method 2 For the second method, I used the equations below: τ = I * α P = τ * ω ==> P = I * α * ω First I calculated my angular acceleration. α = (ωf - ωi)/t = ωf/t The equation simplifies to ωf/t since we are starting from rest. I then input this into my power equation using the moment of inertia of a disc once again. This time I get: P = (1/2)*(mr^2)*(ωf/t)*ωf = [(1/2)*(mr^2)*ωf^2]/t As you can see, my two results differ by the number in the denominator. I have the first equation being multiplied by (1/4) and the second multipled by (1/2). Does anyone know if I am missing any steps in one of these equations that might cause me to miss there being another 2 being multiplied. Any help would be appreciated!