How long does it take for a tape recorder to wind a coil of tape (that is, the total radius is three times of the radius of the empty shaft) with the same length and thickness of 1 / 2 tape The belt shaft rotates at constant angular speed··· It's not as simple as you think. The axis of the belt turns thicker and thicker. The angular velocity is constant, but the change rate of the linear velocity is different. Because the radius changes, the answer seems to cry ···

How long does it take for a tape recorder to wind a coil of tape (that is, the total radius is three times of the radius of the empty shaft) with the same length and thickness of 1 / 2 tape The belt shaft rotates at constant angular speed··· It's not as simple as you think. The axis of the belt turns thicker and thicker. The angular velocity is constant, but the change rate of the linear velocity is different. Because the radius changes, the answer seems to cry ···

If the radius of the empty axis is r, the thickness of the thick tape is D, and the total radius of the thin tape is r, then 9R ^ 2-r ^ 2 = 2 * (R ^ 2-r ^ 2), r = (radical 5) * r thick tape has 2R / D layers, and thin tape [(radical 5) - 1] R / 0.5d = 2 [(radical 5) - 1] R / D layers have the same angular velocity