Final answer:
To calculate the angular acceleration of the ultracentrifuge, we first convert 99700 rpm to radians per second and then divide by the time interval in seconds, resulting in an angular acceleration of 77.40 rad/s².
Step-by-step explanation:
To find the angular acceleration (α) of an ultracentrifuge, we can use the formula α = Δω/Δt, where Δω is the change in angular velocity, and Δt is the change in time.
First, we convert the final velocity from rpm (revolutions per minute) to rad/s (radians per second):
99700 rpm = 99700 rev/min × (2π rad/rev) × (1 min/60 s) = 10448.93 rad/s
Since the ultracentrifuge starts from rest, its initial angular velocity is 0 rad/s. Therefore, the change in angular velocity (Δω) is:
Δω = 10448.93 rad/s - 0 rad/s = 10448.93 rad/s
Now, we convert the time from minutes to seconds:
Δt = 2.25 min × (60 s/min) = 135 s
Finally, we can calculate the angular acceleration (α):
α = Δω/Δt = 10448.93 rad/s / 135 s = 77.40 rad/s²
Therefore, the angular acceleration of the ultracentrifuge is 77.40 rad/s².