# Vertical circular motion with accelerating centre

In summary, the conversation discusses how to solve a problem involving a moving center. The suggested steps include calculating velocity at the topmost position and applying mechanical energy conservation. It is also mentioned that the use of non-inertial frames and pseudo forces can be an easier option. Overall, the conversation concludes that applying a pseudo force and following the suggested steps is the recommended approach for solving the problem.
Homework Statement
Suppose, a ball of mass m has to just complete the vertical circular motion when its point of suspension is accelerating vertically upwards with an acceleration g/3. We have to find that particular minimum speed at the extreme bottom that must be given to it so that it just completes the vertical circle.
Relevant Equations
General laws of motion and energy conservation
I can do the problem if the centre is fixed. The steps are:
1) Assuming tension in the string is zero at the top most position, we calculate the velocity at top most position by mv2/R = mg
2)Now, we simply apply mechanical energy conservation when the ball is at the top and bottom positions respectively and find out the required speed.
But, now as the centre is accelerating, I am confused. Do I have to apply pseudo force and proceed in the same way?
Thanks.

Do I have to apply pseudo force and proceed in the same way?
The use of non inertial frames (and hence pseudo forces) is certainly an option, and probably the easier way here.

So, I should apply pseudo force and follow the two steps, isn't it?

So, I should apply pseudo force and follow the two steps, isn't it?
Yes.

## 1. What is vertical circular motion with accelerating centre?

Vertical circular motion with accelerating centre is a type of motion where an object moves in a circular path with a constant change in its speed. This change in speed is caused by an accelerating centre, which means that the object is constantly changing its direction and velocity.

## 2. What is the difference between vertical circular motion with accelerating centre and uniform circular motion?

In uniform circular motion, the object moves in a circular path at a constant speed, while in vertical circular motion with accelerating centre, the speed of the object changes due to an accelerating centre. Additionally, the direction of the acceleration in vertical circular motion is constantly changing, while it remains constant in uniform circular motion.

## 3. How is the centripetal force related to vertical circular motion with accelerating centre?

The centripetal force is the force that keeps an object moving in a circular path. In vertical circular motion with accelerating centre, the centripetal force is constantly changing as the object moves, since the direction and magnitude of the force is related to the changing velocity of the object. The centripetal force is always directed towards the centre of the circular path.

## 4. What is the role of gravity in vertical circular motion with accelerating centre?

Gravity plays a significant role in vertical circular motion with accelerating centre. It is the force that causes the object to accelerate towards the centre of the circular path. Without gravity, the object would continue moving in a straight line instead of following a circular path.

## 5. How does the radius of the circular path affect vertical circular motion with accelerating centre?

The radius of the circular path has a direct impact on the speed and centripetal force of an object in vertical circular motion with accelerating centre. A larger radius will result in a lower speed and a smaller centripetal force, while a smaller radius will result in a higher speed and a larger centripetal force.

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