Radial Acceleration

In summary, to find the required angular velocity of an ultracentrifuge in \frac{rev}{min}, you would use the formula a_{rad} = (\omega)^{2}r and solve for \omega by converting the given acceleration to rad/s and then to rev/min using the conversion factors 1 rad = \frac{1}{2\pi} rev and 1 s = \frac{1}{60} min. This would result in an angular velocity of \frac{30}{\pi} rev/min.
  • #1
courtrigrad
1,236
2
Find the required angular velocity of an ultracentrifuge in [itex] \frac{rev}{min} [/itex] for the radial acceleration of a point 1.00 cm from the axis to equal 400,000g (that is, 400,000 times the acceleration of gravity.)
So [tex] a_{rad} = (\omega)^{2}r [/tex]. [tex] 400,000g = \omega^{2}(0.01 m) [/tex]. Would I just solve for [tex] \omega [/tex]? [tex] \omega [/tex] would be in m/s? Then to convert to rev/min, you use the fact that [tex] 2\pi(0.01 m) [/tex] equals 1 revolution?
Would this be the correct way to solve this problem?
Thanks
:smile: [
 
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  • #2
when you solve for [itex]\omega[/itex] with your formula the units is [itex]rad/s[/itex] (if you worked in SI units), which needs to be converted to [itex]rev/min[/itex] now
[tex]2\pi\ rad=\ 1\ rev[/tex]
therefore
[tex]1\ rad=\ \frac{1}{2\pi}\ rev[/tex]
and since
[tex]60\ s=\ 1\ min[/tex]
it follows that
[tex]1\ s=\ \frac{1}{60}\ min[/tex]
therefore
[tex]\omega\ =\ \frac{1\ rad}{1\ s}\ =\ \frac{60\ rev}{2\pi\ min}\ =\ \frac{30}{\pi}\ rev/min[/tex]
 
  • #3
Response]

Yes, your approach is correct. To solve for \omega , you would use the equation a_{rad} = (\omega)^{2}r and plug in the given values to solve for \omega . This would give you the angular velocity in units of radians per second (rad/s). To convert to revolutions per minute (rev/min), you can use the conversion factor 2\pi(0.01 m) = 1 revolution, and then convert the angular velocity from rad/s to rev/min. This will give you the required angular velocity of the ultracentrifuge in order to achieve a radial acceleration of 400,000g at a point 1.00 cm from the axis.
 

What is radial acceleration?

Radial acceleration is the rate of change of an object's velocity as it moves along a curved path. It is the component of acceleration that is directed towards the center of the curve.

How is radial acceleration calculated?

Radial acceleration can be calculated using the formula ar = v2/r, where ar is the radial acceleration, v is the velocity, and r is the radius of the curve.

What is the difference between tangential acceleration and radial acceleration?

Tangential acceleration is the rate of change of an object's speed along a curved path, while radial acceleration is the rate of change of the direction of an object's velocity. Tangential acceleration is parallel to the curve, while radial acceleration is perpendicular to it.

What factors affect radial acceleration?

The factors that affect radial acceleration include the object's mass, speed, and the radius of the curve it is traveling along. A larger mass or higher speed will result in a greater radial acceleration, while a larger radius will result in a smaller radial acceleration.

What are some real-world examples of radial acceleration?

Some real-world examples of radial acceleration include a car turning a corner, a roller coaster moving along a curved track, and a satellite orbiting around a planet. In all of these cases, the objects are experiencing a change in direction and therefore a radial acceleration.

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