# Non-Uniform Circular Motion problem

• Zipzap
In summary, the ball swings in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9° past the lowest point on its way up, its total acceleration is (-22.5 i + 20.2j) m/s^2. At that instant, a) sketch a vector diagram showing the components of its acceleration, b) determine the magnitude of its radial acceleration, and c) determine the speed and velocity of the ball.
Zipzap
"Non-Uniform Circular Motion" problem

## Homework Statement

A ball swings in a vertical circle at the end of a rope 1.50 m
long. When the ball is 36.9° past the lowest point on its
way up, its total acceleration is (-22.5 i + 20.2j) m/s^2. At
that instant, (a) sketch a vector diagram showing the components
of its acceleration, (b) determine the magnitude
of its radial acceleration, and (c) determine the speed and
velocity of the ball.

a = v^2 / r

## The Attempt at a Solution

For starters, I don't even know how to approach a), in all honesty. Since the problem doesn't tell me in which direction the rope is spinning, I don't know where to start. However, I have a feeling that the problem doesn't need to tell me this based on the information regarding total acceleration.
Also, even though the total acceleration is expressed in that format, I seriously doubt that the unit vectors are ar and at. If I knew how to draw this, I'll probably be able to figure out the rest of the problem...

It's a vertical circle.There is the weight of the ball downwards and tension of string at an angle.
And yes the unit vectors i and j are not along the radial and transverse directions. If you would draw the problem keeping in mind that the plane of the circle is vertical it would be easier.

All right, I get that much. However, I'm still unable to determine if it's 36.9o to the left, or to the right...

How does it matter?

[PLAIN]http://photos-a.ak.fbcdn.net/hphotos-ak-snc1/hs030.snc1/3190_91017112564_509877564_2512520_5779508_n.jpg

According to this solution, it does...

Last edited by a moderator:

Bump.

I don't mean to offend anybody, but can anyone explain why the solution goes 36.9 degrees to the right, and no to the left?

If you were to look at the setup from the other side the rope would go left. If the diagram is already sketched there is no harm in referring the directions as left or right for convenience.

So you're saying that I could draw it in either direction, and I could still get the diagram, along with b) and c) correct. Am I following you correctly?

Bump...

yes.

## 1. What is non-uniform circular motion?

Non-uniform circular motion is the motion of an object moving in a circular path at a varying speed. This means that the object is not moving at a constant rate, but rather its velocity is changing as it moves along the circular path.

## 2. What causes non-uniform circular motion?

Non-uniform circular motion is caused by a combination of centripetal force and tangential acceleration. Centripetal force is the force that keeps an object moving in a circular path, while tangential acceleration is the change in velocity tangent to the circular path.

## 3. How is non-uniform circular motion different from uniform circular motion?

In uniform circular motion, the speed of the object remains constant while its direction changes, resulting in a circular path. In non-uniform circular motion, the speed of the object is constantly changing, resulting in a varying radius of the circular path.

## 4. How can non-uniform circular motion be calculated?

Non-uniform circular motion can be calculated using the equations for centripetal force and tangential acceleration. These equations can be derived using Newton's laws of motion and the principles of circular motion.

## 5. What are some real-life examples of non-uniform circular motion?

Some examples of non-uniform circular motion in everyday life include a car going around a curved road, a rollercoaster, a spinning top, or a satellite orbiting around the Earth.

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