Final answer:
The angular acceleration of the ultracentrifuge is 87.26 rad/s². The tangential acceleration of a point 9.50 cm from the axis of rotation is approximately 10,024 m/s². The radial acceleration of this point at full rpm is approximately 8.29 m/s² and 0.845 g.
Step-by-step explanation:
(a) To find the angular acceleration, we need to convert the final and initial angular velocities from rpm to rad/s. The final angular velocity is given as 100,000 rpm, which is equivalent to 10,471 rad/s. The initial angular velocity is 0 rpm, so the change in angular velocity is simply the final angular velocity. The time taken to achieve this change in angular velocity is given as 2 minutes, or 120 seconds. Using the formula for angular acceleration (α = (ω_f - ω_i) / t), we can substitute the values to find the angular acceleration:
α = (10,471 rad/s - 0 rad/s) / 120 s = 87.26 rad/s².
(b) The tangential acceleration of a point at a distance of 9.50 cm from the axis of rotation can be found using the centripetal acceleration formula, which is given by a_t = rω², where r is the distance from the axis of rotation and ω is the angular velocity in rad/s. Converting the distance to meters, we have:
a_t = (0.095 m) * (10,471 rad/s)² ≈ 10,024 m/s².
(c) The radial acceleration of the point at full rpm can be found using the formula a_r = rα, where r is the distance from the axis of rotation and α is the angular acceleration in rad/s². Converting the distance to meters, we have:
a_r = (0.095 m) * (87.26 rad/s²) ≈ 8.29 m/s². To find the acceleration in multiples of g, we divide this value by the acceleration due to gravity (g = 9.8 m/s²):
a_r = 8.29 m/s² ÷ 9.8 m/s² ≈ 0.845 g.