Calculating Circular Motion: Distance, Speed, Acceleration, and Period [SOLVED]

In summary, the conversation is about a problem involving a rotating fan and the tip of one of its blades. The question asks for the distance the tip moves in one revolution, the tip's speed and acceleration, and the period of the motion. The person is struggling with finding the equation to use for part (a), but eventually figures out the solution on their own.
  • #1
shell4987
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[SOLVED] Circular Motion

Homework Statement


A rotating fan completes 1170 revolutions every minute. Consider the tip of a blade, at a radius of 18.0 cm. (a) Through what distance does the tip move in one revolution? What are (b) the tip's speed and (c) the magnitude of its acceleration? (d) What is the period of the motion?


Homework Equations


I don't know exactly how to do these problems whatsoever because my professor didn't explain it too well. I know some circular motion formulas such as: a= the square root of ax squared + ay squared = (v squared/r) the square root of cos squared + sin squared = (v squared/r)= v squared/r.


The Attempt at a Solution


I don't even know where to start with this problem or know an equation that includes distance for part (a). It would be great if anyone knew how I could start this problem and if those equations seem right for this problem.
 
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  • #2
Surely you can attempt (a) at least? What is the circumference of a circle?
 
  • #3
Yes, I got part (a) to be 1.13 meters (113cm), but what formula do I use to compute both the speed and acceleration?
 
  • #4
Actually, thank you very much for your help, I ended up trying a few things and figured out how to do this problem on my own.
 

1. How do you calculate the distance of an object in circular motion?

In circular motion, the distance of an object can be calculated using the formula: d = 2πr, where r is the radius of the circular path. This formula assumes that the object completes one full revolution around the circle.

2. How do you calculate the speed of an object in circular motion?

The speed of an object in circular motion can be calculated using the formula: v = 2πr / t, where r is the radius of the circular path and t is the time taken to complete one full revolution around the circle. Alternatively, if the angular velocity (ω) of the object is known, then the linear speed can be calculated using the formula: v = rω.

3. How do you calculate the acceleration of an object in circular motion?

The acceleration of an object in circular motion can be calculated using the formula: a = v² / r, where v is the speed of the object and r is the radius of the circular path. This formula represents the centripetal acceleration, which is always directed towards the center of the circle.

4. How do you calculate the period of an object in circular motion?

The period of an object in circular motion can be calculated using the formula: T = 2πr / v, where r is the radius of the circular path and v is the speed of the object. This formula represents the time taken for one full revolution around the circle.

5. How are the formulas for distance, speed, acceleration, and period related in circular motion?

The formulas for distance, speed, acceleration, and period in circular motion are all interrelated and depend on each other. For example, the speed of an object is directly proportional to its distance from the center of the circle and inversely proportional to its period. Similarly, the acceleration of an object is directly proportional to its speed squared and inversely proportional to its distance from the center of the circle. The period is also inversely proportional to the speed and directly proportional to the distance from the center of the circle.

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