# What is the perpendicular component of the rate of change?

• ohheytai
In summary, the child's mass, velocity, and length of the elastic cord are given. The question is asking for the perpendicular component of the rate of change of the child's momentum, which can be calculated using the equation mv^2/r. However, the result of 214.05 is incorrect. Further assistance is needed to find the correct solution.
ohheytai
A child of mass 22 kg swings at the end of an elastic cord. At the bottom of the swing, the child's velocity is horizontal, and the speed is 6 m/s. At this instant the cord is 3.70 m long.

At this instant, what is the perpendicular component of the rate of change of the child's momentum?

mv^2/r

## The Attempt at a Solution

i tried 22*6^s divded by 3.70
and got 214.05. but its wrong can someone help me please thanks!

ohheytai said:
A child of mass 22 kg swings at the end of an elastic cord. At the bottom of the swing, the child's velocity is horizontal, and the speed is 6 m/s. At this instant the cord is 3.70 m long.

At this instant, what is the perpendicular component of the rate of change of the child's momentum?
you mean the horizontal component is 0, don't you? But regardless of what the horizontal component is, the problem is asking for the perpendicular component of the rate of change of the child's momentum, which is the net force acting on the child in the centripetal direction, for which it appears you have, by chance or intent, the correct equation.

mv^2/r

## The Attempt at a Solution

i tried 22*6^s divded by 3.70
and got 214.05. but its wrong can someone help me please thanks!
Maybe it's a significant figure thing? Try 210, no decimal points please, and don't forget the units associated with this number!

## 1. What is the perpendicular component of the rate of change?

The perpendicular component of the rate of change is the component of the rate of change that is perpendicular to the direction of the motion or change. It is often referred to as the "normal" component and is calculated using trigonometric functions.

## 2. How is the perpendicular component of the rate of change calculated?

The perpendicular component of the rate of change is calculated by finding the dot product of the rate of change vector and a unit vector that is perpendicular to the direction of motion. This can also be calculated using trigonometric functions and the angle between the two vectors.

## 3. Why is the perpendicular component of the rate of change important?

The perpendicular component of the rate of change is important because it allows us to understand the change in a system or object in a specific direction. It also helps us understand the relationship between different components of motion and how they contribute to overall change.

## 4. Can the perpendicular component of the rate of change be negative?

Yes, the perpendicular component of the rate of change can be negative. This occurs when the rate of change vector and the perpendicular unit vector are in opposite directions, resulting in a negative dot product. This indicates that the motion is in the opposite direction of the perpendicular unit vector.

## 5. In what situations is the perpendicular component of the rate of change used?

The perpendicular component of the rate of change is used in various fields of science and engineering, such as physics, mechanics, and fluid dynamics. It is particularly useful in analyzing rotational motion, fluid flow, and the behavior of objects moving in a curved path.

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