How would I go about computing the radial acceleration when given i and j components?

In summary, the conversation discusses a problem involving a ball swinging in a vertical circle at the end of a rope. The question asks to find the radial acceleration and velocity at a specific point in the motion. The attempt at a solution involves calculating the total acceleration and using trigonometric functions to find the radial component and velocity.
  • #1
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Homework Statement


I attempted this problem, and i have a midterm tommorow. I thought my approach was correct but I don't have a clue if it actually is. I drew a simple right angle triangle according to the information given in the question.

A ball swings in a vertical circle at the end of a rope 1.40 m long. When the ball is 36.1° past the lowest point on its way up, its total acceleration is (−22.5i + 20.2j ) m/s^2. For that instant, do the following. Find the radial acceleration. Also compute the velocity at this acceleration

Homework Equations



l a l = √(ai^2 + aj^2) , ar=v^2/r

The Attempt at a Solution



l a l= √(-22.5)^2+(20.2)^2=30.24

ar=30.24cos36.1

v=√(30cos36.1)(1.4) = 5.8
 
Last edited:
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  • #2
welcome to pf!

hi samatar! welcome to pf! :wink:

no, the radial component of acceleration will be the total acceleration "dot" the unit vector in the radial direction

try again :smile:​
 

Related to How would I go about computing the radial acceleration when given i and j components?

1. What is radial acceleration?

Radial acceleration is the component of acceleration that is directed towards or away from the center of a circular or curved path. It is perpendicular to the tangential acceleration, which is directed along the path of motion.

2. How do I calculate radial acceleration?

To calculate radial acceleration, you need to know the tangential velocity and the radius of the circular or curved path. You can use the formula: ar = v2/r, where ar is the radial acceleration, v is the tangential velocity, and r is the radius of the path.

3. What are the i and j components of radial acceleration?

The i and j components of radial acceleration refer to the x and y axes, respectively. In other words, the i component is the acceleration in the horizontal direction and the j component is the acceleration in the vertical direction.

4. How do I find the i and j components of radial acceleration?

To find the i and j components of radial acceleration, you can use trigonometric functions. The i component is calculated by multiplying the radial acceleration by the cosine of the angle between the radial acceleration and the x-axis. The j component is calculated by multiplying the radial acceleration by the sine of the angle between the radial acceleration and the y-axis.

5. Can I use a calculator to compute radial acceleration?

Yes, you can use a calculator to compute radial acceleration as long as you have all the necessary information, such as the tangential velocity and radius of the path. Make sure to use the correct formula and units when entering the values into the calculator.

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