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) What is the centripetal acceleration, in m/s^2, of this point at full rpm?
(d) Express this centripetal acceleration as a multiple of g.
(a) First, convert 100,000 rpm to rad/s:
100,000 rpm = 100,000/60 rad/s = 1666.67 rad/s
Next, use the formula for angular acceleration:
a = (v^2)/r
a = (1666.67^2)/13.30
a = 10486061.112/13.30
a ≈ 787580.07 rad/s^2
(b) To find the tangential acceleration, we use the formula:
a_t = r * a
a_t = 0.1330 * 787580.07
a_t ≈ 104669.67 m/s^2
(c) The centripetal acceleration is equal to the tangential acceleration:
a_c = 104669.67 m/s^2
(d) To express this centripetal acceleration as a multiple of g, divide it by the acceleration due to gravity:
a_c = 104669.67 m/s^2 / 9.81 m/s^2
a_c ≈ 10672.49 g
So, the centripetal acceleration of the point at full rpm is approximately 10672.49 times the acceleration due to gravity.