# Circular Motion Problem -- Ball on a String Spinning in a Vertical Circle

• Al-Layth
In summary, circular motion is the movement of an object along a circular path, where the distance from the center of the circle remains constant. This type of motion can be found in objects like a ball rolling in a circular track or planets orbiting around a star. In the case of a ball on a string spinning in a vertical circle, the fixed point is the point where the string is attached to a pivot. The ball moves along a circular path while the string remains taut, creating a uniform circular motion. The factors that affect the circular motion of a ball on a string include the mass of the ball, the length of the string, the speed at which the ball is spinning, and the force of gravity acting on the ball. The

#### Al-Layth

Homework Statement
A ball of 5.0 kg mass is attached to the end of a long wire and whirled around in a perfect
circle of 0.9 m radius in the vertical plane. Calculate the following:

Calculate the Minimum Velocity and Minimum Angular Velocity
Relevant Equations
#F= m\frac{v^2}{r} = mw^{2}r#

#m: Mass#
#v: Speed#
#w: Angular Velocity#
#F= m\frac{v^2}{r} = mw^{2}r#

#m=5#
#r=0.9#

#F= 5\frac{v^2}{0.9} = (0.9)5w^{2}#

#5\frac{v^2}{0.9} = (0.9)5w^{2}#

#\frac{v^2}{0.9} = (0.9)w^{2}#

#v=0.9w#

then I get stuck cause I have both unknowns in one equations (i bet it has something to do with the question’s use of “minimum” but I don’t know where to go from here) so help mee thx

The question says the circle is in the vertical plane. What else do you have to take account of in this case?

Where is the velocity minimal? What is required for the string to be taut there?

## 1. What is circular motion?

Circular motion is the movement of an object along a circular path. It occurs when an object travels at a constant speed along a circular path, with the direction of motion constantly changing.

## 2. How does a ball on a string spinning in a vertical circle work?

A ball on a string spinning in a vertical circle is a classic example of circular motion. The ball is attached to a string and is swung in a vertical circle. The string provides the centripetal force needed to keep the ball moving in a circular path, while the ball's inertia causes it to resist changes in its motion, resulting in the circular motion.

## 3. What is the relationship between the speed of the ball and the radius of the circle?

The speed of the ball on a string spinning in a vertical circle is directly proportional to the radius of the circle. This means that as the radius increases, the speed of the ball also increases, and vice versa.

## 4. How does the weight of the ball affect its motion in a vertical circle?

The weight of the ball affects its motion in a vertical circle by providing the necessary force for the ball to move in a circular path. The weight of the ball acts as the centripetal force, keeping the ball moving in a circular path, and is dependent on the mass of the ball and the speed of its motion.

## 5. What is the difference between centripetal force and centrifugal force?

Centripetal force is the force that keeps an object moving in a circular path, while centrifugal force is the apparent outward force experienced by an object in circular motion. Centrifugal force is not a real force, but rather a result of the inertia of the object resisting changes in its motion. In the case of a ball on a string spinning in a vertical circle, the centripetal force is provided by the tension in the string, while the centrifugal force is the apparent outward force experienced by the ball.