Question

For a centrifuge rotating at 2.69e+3 rpm (rpm = revolutions per minute) with a radius of 1.79 cm, what is the centripetal acceleration expressed in g-force

Answer 1

The centrifuge rotating at 2690 rpm with a 1.79 cm radius provides a centripetal acceleration of approximately 144.74g.

Step-by-step explanation:

To find the centripetal acceleration in g-force for a centrifuge rotating at 2690 rpm with a radius of 1.79 cm, we must first convert the angular velocity from rpm to rad/s. Then, we use the formula ac = rω² to calculate the centripetal acceleration, where ac is the centripetal acceleration, r is the radius of the centrifuge, and ω (omega) is the angular velocity in rad/s.

• Convert rpm to rad/s: ω = 2690 rpm × (2π rad/rev) × (1 min / 60 s) = 281.62 rad/s.
• Convert cm to m: r = 1.79 cm = 0.0179 m.
• Calculate centripetal acceleration: ac = 0.0179 m × (281.62 rad/s)² = 1419.89 m/s².
• Convert to g-force: g = 9.81 m/s², so ac in g's is ac/g = 1419.89 m/s² / 9.81 m/s² = 144.74g.

The centrifuge provides a centripetal acceleration of approximately 144.74g to a point at its edge.