Physics frustration!!!?

Question

Starting from rest, a 12-cm-diameter compact disk takes 3.0 s to reach its operating angular velocity of 2000 rpm. Assume that the angular acceleration is constant. The disk's moment of inertia is .

How many revolutions does it make before reaching full speed?

I found the alpha, which is 0.001745
Then I used one of the kinematics equations to find theta, and I converted the radians answer to rev, I got 0.00125 but it's the wrong answer.

Can you provide the answer and how you did it. Thanks

Answer 1

omega(t) = 2000 * t/3 * 2*pi/60.

The angle rotated in 3 seconds is:

theta(3) = int(from 0 to 3) (omega(t) dt) =
= 2000/2*3* 2*pi/60.

N_turns = theta(3)/(2pi) = 3000/60 = 50 turns.

Easy way:

2000 RPM * 3 sec / 60 sec/min / 2 = 50 turns

(Remember that mean speed = final speed/2).

Answer 2

w = alpha T; where w = 2000 rpm = 2 pi radian/rev * 2000 rev/min * (1/60 min/sec) = ? rad/sec You can do the math to convert rps to rad/sec. T = 3 sec, time to rev up to speed.

Solve for alpha = w/T in rad/sec^2.

Then w^2 = 2 alpha theta; where theta is the distance in radians traveled to get to w when accelerating. Thus, w^2 = 2 (w/T) theta; so that w = 2(1/T) theta and theta = wT/2 in radians traveled. Divide theta by 2 pi rad/rev to get the number of revs = N = theta/2pi. You can do the math.

The physics is this. Theta is just the average angular velocity (w/2) times the time of the acceleration T when accelerating at a constant angular acceleration and starting from a stop.

Answer 3

lawda tumhaara maa ka choot.....!!!!!