Circular motion- how slowly would you twirl the ball in vertical circle

In summary, the critical speed for a ball attached to a cord in a vertical circle is reached when the tension in the cord is zero. The slowest speed for an 800-g ball to complete a vertical circle with a radius of 1 m can be found using the equation v=√gR, resulting in a speed of 3.13 m/s.
  • #1
dani123
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Homework Statement



If you twirl a ball attached to a cord in a vertical circle, there would be a critical speed at the top for which the tension in the cord is zero. This is because the force of gravity supplies all the centripetal force necessary to complete the circle. How slowly would you twirl an 800-g ball so that it would describe a vertical circle of radius 1 m?

Homework Equations



Because we are looking for the slowest speed that the ball can have in order to complete the circle Fg=Fc
And therefore, through rearranging equations found that v=√gR

The Attempt at a Solution



So from that manipulated equation found that v=3.13m/s

If anyone could just verify my answer, that would be greatly appreciated! Thank you so much for your help and time!
 
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  • #2
Looks okay to me.
 

FAQ: Circular motion- how slowly would you twirl the ball in vertical circle

How does the speed of the ball affect the circular motion in a vertical circle?

The speed of the ball does not affect the circular motion in a vertical circle. The only factor that affects the motion is the force acting on the ball, which is the tension in the string.

Is there a minimum speed required to keep the ball in circular motion in a vertical circle?

Yes, there is a minimum speed required to keep the ball in circular motion in a vertical circle. If the speed is too low, the ball will fall out of the circle due to gravity. This minimum speed is dependent on the radius of the circle and the acceleration due to gravity.

How does the radius of the circle affect the speed needed for circular motion in a vertical circle?

The radius of the circle does not directly affect the speed needed for circular motion in a vertical circle. However, a larger radius will require a higher speed to overcome the force of gravity and keep the ball in the circle. On the other hand, a smaller radius will require a lower speed for the same reason.

Can the direction of the circular motion in a vertical circle be changed?

Yes, the direction of the circular motion in a vertical circle can be changed. This can be done by changing the orientation of the string or by changing the direction of the force acting on the ball. The ball will continue to move in the new direction as long as the force is still present.

What is the relationship between the frequency of the circular motion and the speed of the ball in a vertical circle?

The frequency of the circular motion is directly proportional to the speed of the ball in a vertical circle. This means that as the speed increases, the frequency also increases, and vice versa. This relationship is described by the equation f = v/2πr, where f is the frequency, v is the speed, and r is the radius of the circle.

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