Calculate the centripetal acceleration of a point 7.50 cm from the axis of an ultracentrifuge whose angular velocity works out to 7854 rad/s.

1. Centripetal acceleration in terms of angular velocity is ac = r * omega^2. 2. Convert the radius to meters first, since 7.50 cm = 0.0750 m. 3. Substitute the values: ac = (0.0750 m)(7854 rad/s)^2. 4. Squaring 7854 rad/s gives about 6.169 x 10^7 rad^2/s^2, and multiplying by 0.0750 m gives ac = 4.63 x 10^6 m/s^2. 5. Dividing this by g = 9.80 m/s^2 gives a ratio of about 472,000, confirming the acceleration is roughly 472,000 times g, far larger than any of the other listed magnitudes. 6. 5.89 x 10^4 m/s^2 and 4.63 x 10^4 m/s^2 are each off by a factor of 100 from a decimal slip in the radius conversion, and 1.05 x 10^8 m/s^2 comes from squaring the radius instead of the angular velocity. _Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.2 Centripetal Acceleration_