An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) what is its angular acceleration in rad/s2 ? (b) what is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) what is the radial acceleration in m/s2 and multiples of of this point at full rpm?

(a) The angular acceleration is given by:

where

is the final angular velocity

is the initial angular velocity

is the time interval

Let's convert the angular velocities in rad/s and the time in seconds:

Substituting the numbers into the equation, we find the angular acceleration:

(b) The tangential acceleration is given by the product between the angular acceleration and the distance of the point from the axis of rotation. In this case, the distance is

Therefore the tangential acceleration is

(c) The radial acceleration (also known as centripetal acceleration) is given by the product between the square of the angular velocity and the distance from the axis of rotation: