Calculate the centripetal acceleration of a point 7.50 cm from the axis of an ultracentrifuge spinning at 7.5 x 104 rev/min.

Answer 1

You can find the centripetal acceleration of an object with the equation a_c = v²/r. Here, a_c is the centripetal acceleration in m/s², v is the speed of the object traveling in a circle in m/s, and r is the radius of your circle in meters.

The centrifuge has an angular velocity of 7.5x10⁴ rev/min = 75,000 rev/min. We can use this information to find the speed of a point 7.50 cm from the axis of the centrifuge. After that, we can find the centripetal acceleration.

Speed = Distance/time. Here, our distance is 75,000 circumferences and our time is 1 minute. We can use circumference = 2πr here. Distance = 75,000 x 2πr = 75,000 x 2π x (7.50 cm) = 3,534,000 cm = 35,340 m. The speed is then 35,340 m/min. Speed in m/s = 35,340/60 = 589 m/s.

Now we just plug into a_c = v²/r: a_c = 589²/0.075 = 4,626,000 m/s².