Radius of centripetal force when on an angle.

In summary, the conversation discusses the correct method for solving a physics problem involving a bead rotating around a hoop. The correct radius to use in the equations is not the radius of the hoop, but rather the distance from the bead to the center of rotation. While one participant initially made a mistake in their calculations, they later corrected it and achieved the correct answer. The conversation also addresses the fact that the radius of the circular path made by the bead is not the same as the radius of the hoop.
  • #1
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http://puu.sh/4IjIT.png [Broken]

I don't quite understand why this is correct. My initial try was this... (the only difference is at the end, bolded)

r = 0.154m
period = 0.426s
rev per second = 1/0.426s
w = 2*pi*(1/0.426)

mg = Fn*cosx
Fn = mg/cosx
Fc = Fn*sinx = mg/cosx
= mg*tanx

mg*tanx = mv^2/r
mg*tanx = m(r*sinx)w^2
g*tanx = (r*sinx)*w^2
9.8*tan(x) = 0.154*sinx*[2*pi*(1/0.426)]^2

EDIT: So this way does work, why did the way in the screenshot get the same answer?
EDIT 2: Oh... I just did it wrong and coincidentally got a close enough answer to round to the right answer.
 
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  • #2
Esoremada said:
So why is the radius of the rotation about the y-axis constantly equal to the given radius of the ring, shouldn't the distance from the bead to the centre of rotation depend on the angle of the bead?

If the bead was at a 1 degree angle from the vertical, the circle of motion it makes would be nowhere near 15cm. I don't get why the radius in the equation mv^2/r or mrw^2 wouldn't be r*sinx.
You are correct. The radius of the circular path made by the bead is not the radius of the hoop.
 
  • #3
Doc Al said:
You are correct. The radius of the circular path made by the bead is not the radius of the hoop.

So why did I get the correct answer by using the full radius of the hoop as the path made by the bead?

When I use my way I get 90 degrees, so it's definitely wrong.

EDIT: Did the math wrong, my way does work.

9.8*tan(x) = 0.154*sinx*[2*pi*(1/0.426)]^2
9.8/cosx = 0.154*[2*pi*(1/0.426)]^2
9.8 = cosx*(0.154*[2*pi*(1/0.426)]^2)
arccos(9.8 / [0.154*[2*pi*(1/0.426)]^2]) = 73
 
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1. What is the formula for calculating the radius of centripetal force when on an angle?

The formula for calculating the radius of centripetal force when on an angle is: r = v^2 / (g * tanθ), where r is the radius, v is the velocity, g is the acceleration due to gravity, and θ is the angle.

2. How do you determine the direction of the centripetal force when on an angle?

The direction of the centripetal force when on an angle is always towards the center of the circle. This means that the force is perpendicular to the velocity of the object and towards the point of rotation.

3. Can the radius of centripetal force change when on an angle?

Yes, the radius of centripetal force can change when on an angle. It depends on the angle, velocity, and acceleration of the object. As these values change, the radius of centripetal force will also change.

4. How does the angle affect the radius of centripetal force?

The angle has a direct impact on the radius of centripetal force. As the angle increases, the radius of centripetal force will decrease. This means that the centripetal force becomes stronger and the object will move in a tighter circle.

5. Can the radius of centripetal force be greater than the radius of the circle?

No, the radius of centripetal force cannot be greater than the radius of the circle. The radius of centripetal force is always equal to or less than the radius of the circle, depending on the angle and other factors. If the centripetal force becomes greater than the radius of the circle, the object will move outwards from the center of the circle.

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