Question kinetic energy in circular motion

In summary, the kinetic energy of an object in uniform circular motion is directly proportional to the centripetal force and the square of the velocity. The relationship between kinetic energy and radius is inverse, as an increase in radius leads to a decrease in kinetic energy. The period of circular motion is not directly proportional to kinetic energy. Therefore, the correct answer is options I and II.
  • #1
410
11

Homework Statement



An object moves in uniform circular motion. Its kinetic energy is directly proportional to:
I. centripetal force
II. radius of the circle
III. the period of circular motion

Homework Equations


I took the universal gravitational law

G* m1 * m2 /r^2 = m2 * v^2/r

and then I rearranged for the kinetic energy of circular motion to get:

G * m1 * m2 /r = m2 * v^2 /2

The Attempt at a Solution



Looking at my equation, I was able to see that the bigger the centripetal force is, the more kinetic energy we have. I is an option.

As the radius gets bigger, the kinetic energy decreases, so II is out.

As the period of circular motion gets bigger, the velocity decreases, to the kinetic energy is not directly proportional.

Thus, I chose only I. However, the solutions say that the answer is I and II.

Why is this the case? Thanks a lot in advance!
 
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  • #2
The question does not mention gravity or orbits, just circular motion. You should work with expressions that apply generally to objects in circular motion.

Start by writing expressions for KE, Fc (Centripetal force) , and T (period) in terms of v and r.
 
  • #3
Never mind. I got it.

Fc = m*v^2/r.

rFc/2 = 0.5 * m * v^2 = K.E.

I see it now. Thanks so much!
 

1. What is kinetic energy in circular motion?

Kinetic energy in circular motion refers to the energy possessed by an object in circular motion due to its velocity. It is a form of energy that is associated with the movement of an object.

2. How is kinetic energy in circular motion calculated?

The formula for calculating kinetic energy in circular motion is: KE = 1/2 * m * v^2, where m is the mass of the object and v is the velocity of the object.

3. Does kinetic energy in circular motion change?

Yes, kinetic energy in circular motion can change. It can increase or decrease depending on the factors that affect it, such as changes in velocity or mass.

4. What is the relationship between kinetic energy and circular motion?

Kinetic energy and circular motion are closely related as kinetic energy is the energy associated with the movement of an object, and in circular motion, the object is continuously moving in a circular path with a certain velocity.

5. How does friction affect kinetic energy in circular motion?

Friction can decrease the kinetic energy in circular motion by causing the object to lose some of its velocity. This is because friction acts against the direction of motion, resulting in a decrease in the object's speed and therefore its kinetic energy.

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