Uniform Circular motion problem,

In summary: It's served me well over the years!In summary, the magnitude of the centripetal acceleration of the particles making up the wind in a hurricane 25km from the eye is 0.10m/s^2. The equation used to calculate this is Ac=V^2/r, where V is the velocity and r is the radius. It is important to convert all units to the mks standard in order to get the correct answer.
  • #1
naham1866
4
0
1. At a distance of 25km from the eye of a hurricane, the wind is moving at 180km/h in a circle. What is the magnitude of the centripetal acceleration, in meters per second squared, of the particles that make up the wind?


Homework Equations


Ac=V^2/r = 4∏^2r/T^2 = 4∏^2rf^2


The Attempt at a Solution


Ac=V^2/r

The answer is 0.10m/s but I just can't seem to get it right.
 
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  • #2
naham1866 said:
1. At a distance of 25km from the eye of a hurricane, the wind is moving at 180km/h in a circle. What is the magnitude of the centripetal acceleration, in meters per second squared, of the particles that make up the wind?


Homework Equations


Ac=V^2/r = 4∏^2r/T^2 = 4∏^2rf^2


The Attempt at a Solution


Ac=V^2/r

The answer is 0.10m/s but I just can't seem to get it right.

You have the right equation in your attempt. Fill in the numbers for velocity V and radius r, and be sure to stay consistent in your units. Show us that work...
 
  • #3
Okay so I got Ac=180km/h^2/25km

Problem is that it doesn't give me 0.10m/s
 
  • #4
naham1866 said:
Okay so I got Ac=180km/h^2/25km

Problem is that it doesn't give me 0.10m/s

You need to fix the units. You need to convert everything into meters, kilograms and seconds (the mks standard SI system of units). If you mix units like seconds and hours up, you won't get the right answers.

So convert everything you are given into mks units, and plug those quantities into the equation. Carry units along in the equation, and if you have the same units in numerator and denominator, you can cancle them out. Like m/m = 1, and s^2/s = s, and so on.

Now show us what you get...
 
  • #5
Haha YES! I Did it! I went out and on my way back home I remembered that I had to change from kilometers to meters, so here's what I did.

180km/h / 60 = 3m/min /60 = 0.05m/s
25km / 1000 = 0.025m
Ac = V^2/r
Ac = 0.05m/s^2/0.025m
Ac= .10m/s
YES! :D
 
  • #6
Thank you vey much for the help
 
  • #7
naham1866 said:
Thank you vey much for the help

You are welcome. Learning to carry units along in your calculations is a huge trick, IMO. I still remember the first time I learned that wey back in undergrad many years ago.
 

Related to Uniform Circular motion problem,

1. What is uniform circular motion?

Uniform circular motion is the movement of an object in a circular path at a constant speed. This means that the object is moving at the same speed and direction throughout its motion.

2. What are the forces involved in uniform circular motion?

The two main forces involved in uniform circular motion are centripetal force and centrifugal force. Centripetal force acts towards the center of the circle and keeps the object moving in a circular path, while centrifugal force acts in the opposite direction and is caused by the object's inertia.

3. How is uniform circular motion different from linear motion?

In linear motion, an object moves in a straight line at a constant speed. In uniform circular motion, the object moves in a circular path at a constant speed. This means that the direction of the object's velocity is constantly changing in uniform circular motion, whereas it remains constant in linear motion.

4. What is the role of velocity and acceleration in uniform circular motion?

In uniform circular motion, the velocity of an object is constantly changing as it moves in a circular path. However, its speed remains constant. The acceleration in uniform circular motion is directed towards the center of the circle and is responsible for changing the direction of the object's velocity.

5. How is uniform circular motion related to Newton's laws of motion?

The first law of motion states that an object will remain in a state of rest or uniform motion unless acted upon by an external force. In uniform circular motion, the centripetal force acts as the external force that keeps the object moving in a circular path. The second law of motion relates the acceleration of an object to the force and mass of the object, which can be seen in the equation a = F/m for uniform circular motion. The third law of motion states that for every action, there is an equal and opposite reaction. In uniform circular motion, this is seen in the relationship between centripetal and centrifugal forces acting on the object.

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