More with Centripetal Acceleration

• rockmorg
In summary, the question is asking for the magnitude of the centripetal acceleration at the wall of a kitchen gadget that dries lettuce leaves. The gadget has a radius of 10 cm and is rotating at 1.9 revolutions per second. Using the equation v = 2πr/T, the linear velocity is calculated to be 0.330 m/s. Then, using the formula Ac = v^2/r, the centripetal acceleration is found to be 1.1 m/s^2. The issue with the given information is that revolutions per second is a frequency, not a time unit, so it needs to be converted to a period (T) of 1/1.9 seconds in order to correctly
rockmorg
Hey again all - I think I have another problem where my math skills just aren't cutting it --

Kitchen gadget that dries lettuce leaves by spinning them, the radius of the container is 10 cm and it is rotating at 1.9 revolutions per second. Magnitude of centripetal acceleration at the wall?

r = 10 cm (.1 m)
rps = 1.9
Ac = ?

1.9 rev/1 sec = 1.9 sec?

So I use v = 2Pir/T

v = 2Pi(.1 m)/1.9 s
v = .330 m/s

Ac = v2/r = (.330 m/s)2/.1 m = .1089/.1 = 1.1 m/s2

I have a feeling the problem is the revolutions per second, like I'm not converting that into the correct amount for one revolution...

Any thoughts?

Thanks!

Hi rockmorg,
rev/s is a frequency so if $$\nu=1.9 s^{-1}$$ the period (T) will be $$1/1.9$$ because of $$\nu=1/T$$

I would suggest using the correct units in your calculations to avoid confusion. In this case, it would be helpful to convert the revolutions per second into radians per second, as one revolution is equal to 2π radians. So, 1.9 rev/s would be equivalent to 1.9 x 2π = 3.8π rad/s.

With this conversion, your calculation for velocity would be:

v = 2π(.1 m)(3.8π rad/s) = 3.8 m/s

And your calculation for centripetal acceleration would be:

Ac = v^2/r = (3.8 m/s)^2/.1 m = 14.44 m/s^2

I hope this helps and remember to always double check your units to ensure accurate calculations.

What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It always points towards the center of the circle and is calculated using the formula a = v^2/r, where v is the velocity of the object and r is the radius of the circle.

How is centripetal acceleration different from tangential acceleration?

Centripetal acceleration is the acceleration towards the center of a circle, while tangential acceleration is the acceleration in the direction of motion. They are perpendicular to each other and together make up the total acceleration of an object moving in a circular path.

What factors affect the magnitude of centripetal acceleration?

The magnitude of centripetal acceleration is affected by the speed of the object and the radius of the circle it is moving in. The higher the speed or the smaller the radius, the greater the centripetal acceleration.

Can centripetal acceleration be negative?

No, centripetal acceleration is always positive as it is a measure of the change in velocity towards the center of the circle. Negative acceleration would indicate a change in velocity away from the center.

How is centripetal acceleration used in real life?

Centripetal acceleration is used in many real-life applications such as amusement park rides, car racing, and satellite orbits. It is also important in understanding the forces acting on objects in circular motion, such as the tension in a string or the friction between a car's tires and the road.

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