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