Calculating Centripetal Acceleration & Tension in Circular Motion

In summary, centripetal acceleration is the acceleration experienced by an object moving in a circular path, always directed towards the center of the circle. It can be calculated using the formula a = v^2/r, where v is the velocity and r is the radius. Centripetal acceleration and velocity are directly related, with an increase in velocity resulting in an increase in acceleration. This affects the tension in a string attached to the moving object, with a higher acceleration resulting in a higher tension. Centripetal acceleration can never be negative as it is always directed towards the center of the circle.
  • #1
badboyben03
39
0
An athlete whirls a 6.50-kg hammer tied to the end of a 2.0-m chain in a horizontal circle. The hammer moves at the rate of 1.1 rev/s.

What is the centripetal acceleration of the hammer?
What is the tension in the chain?
 
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  • #2
What have you tried so far?

a = (v^2)/r is a start
 
  • #3
1.1 rev/s is not the velocity right?
 
  • #4
It is, but you must convert to m/s for use in the equation for centripetal acceleration.
 
  • #5
how do you convert it?
 
  • #6
(1.1 rev/s)(2piR meters/rev)
 

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle and its magnitude is given by the formula a = v^2/r, where v is the velocity of the object and r is the radius of the circle.

2. How do you calculate centripetal acceleration?

To calculate centripetal acceleration, you need to know the velocity of the object and the radius of the circle it is moving in. Then, you can use the formula a = v^2/r to find the magnitude of the centripetal acceleration. It is important to note that the direction of the acceleration is always towards the center of the circle.

3. What is the relationship between centripetal acceleration and velocity?

Centripetal acceleration and velocity are directly related. This means that as the velocity of an object increases, the centripetal acceleration also increases. This is because the faster an object is moving in a circular path, the greater the force needed to keep it in that path, resulting in a higher acceleration.

4. How does centripetal acceleration affect tension in a string?

When an object is moving in a circular path attached to a string, the string experiences tension. The magnitude of this tension is equal to the centripetal force required to keep the object in its circular path. Therefore, as the centripetal acceleration increases, so does the tension in the string.

5. Can the centripetal acceleration ever be negative?

No, the centripetal acceleration can never be negative. This is because it is always directed towards the center of the circle, regardless of the direction of the object's velocity. If the object changes direction, the centripetal acceleration will also change direction, but it will always remain positive (or zero if the object is not moving in a circular path).

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