Calculating Average Acceleration in Uniform Circular Motion

In summary, the problem discussed is about finding the magnitude of the average acceleration of a particle moving in a circle of radius r completing one cycle in time T. The speaker believes that over time T, the magnitude of the average acceleration should be zero, but over time T/2, it should be a non-zero number. They explain that this is because the acceleration is constant and the instantaneous acceleration is equal to the average acceleration. The final velocity and initial velocity at time T/2 are equal in magnitude but opposite in direction, resulting in a change in velocity of (2)(magnitude of v). Using the formula v=(2(pi)r)/T, the change in velocity is calculated to be (4(pi)r)/T. With a change
  • #1
LD_90
11
0
I've been working on this for awhile. I think I've got it. Ok here's the problem:

A particle moves in a circle of radius r completing one cycle in time T. What is the magnitude of the average acceleration over time T and over time T/2?

It seems to me that over time T the magitude of the ave acceleration should be zero, but over time T/2, it has to be a non-zero number. Since the acceleration is constant, the instantaneous acceleration should be equal to the average acceleration. v(final)-v(initial)=change in v

the (change in v)/(change in time)= a ; so at time T, v(final) - v(initial)=0 and so acceleration has to equal zero. Over time T/2, v(final ) and v(initial) are equal in magnitude but opposite in direction, so the change in v
should equal (2)(magnitude of v)

v=(2(pi)r)/T, then delta v = (4(pi)r)/T, delta t=T/2, so a=((8)(pi)r)/T^2
This seems right to me. Am I missing something.
 
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  • #2
looks fine to me.
 
  • #3
Thanks for the help.
 

1. What is uniform circular motion?

Uniform circular motion is a type of motion in which an object moves along a circular path at a constant speed. The object's velocity is always tangent to the circle, and its acceleration is directed towards the center of the circle.

2. What is the formula for calculating the speed of an object in uniform circular motion?

The formula for calculating the speed of an object in uniform circular motion is v = 2πr/T, where v is the speed, r is the radius of the circle, and T is the time it takes for the object to complete one full revolution.

3. Is the acceleration of an object in uniform circular motion constant?

Yes, the acceleration of an object in uniform circular motion is constant in magnitude but changes in direction. The direction of the acceleration is always towards the center of the circle, which causes the object to continually change direction.

4. What is the difference between linear and circular motion?

Linear motion is motion in a straight line, while circular motion is motion along a curved path. In linear motion, the velocity and acceleration are in the same direction, while in circular motion, the acceleration is always directed towards the center of the circle.

5. Can an object in uniform circular motion have a constant speed but changing velocity?

Yes, an object in uniform circular motion can have a constant speed but changing velocity. This is because velocity is a vector quantity that includes both speed and direction. In circular motion, the direction of the velocity is constantly changing, even if the speed remains constant.

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