An ultracentrifuge accelerates from rest to 100,000 rpm in 1.20 min. Solve c using the equation a=(v^2)/r

Question

(a) What is its angular acceleration in rad/s^2?
(b) What is the tangential acceleration, in m/s^2, of a point 13.30 cm from the axis of rotation?
(c) If the radial acceleration is 14500000, express it as a multiple of g.

Answer 1

(a) First, we need to convert 100,000 rpm to rad/s.

1 rpm = 2π/60 rad/s
100,000 rpm = (100,000 * 2π)/60 = 10472.8 rad/s

Now, we can calculate the angular acceleration using the formula a = (v^2)/r:

a = (10472.8)^2 / 13.30 cm = 8288733.4 rad/s^2

(b) To find the tangential acceleration, we need to convert the radius to meters:

13.30 cm = 0.133 m

Now, we use the formula for tangential acceleration:

a_t = r * α = 0.133 * 8288733.4 = 1102854.72 m/s^2

(c) Given radial acceleration = 14500000 m/s^2

To express it as a multiple of g, we divide it by the acceleration due to gravity g = 9.81 m/s^2:

Multiple of g = 14500000 / 9.81 ≈ 1479591.84

Therefore, the radial acceleration is approximately 1479592 times the acceleration due to gravity.