Calculating Average Acceleration in Uniform Circular Motion

Click For Summary
SUMMARY

The discussion focuses on calculating the average acceleration of a particle in uniform circular motion with a radius r, completing one cycle in time T. It concludes that the average acceleration over the full period T is zero, as the initial and final velocities are equal, resulting in no change in velocity. However, over the half period T/2, the average acceleration is non-zero, calculated as a = (8πr)/T², due to the change in velocity being twice the magnitude of the velocity vector. The participant confirms the calculations are correct and seeks validation.

PREREQUISITES
  • Understanding of uniform circular motion
  • Familiarity with basic kinematics equations
  • Knowledge of vector addition and subtraction
  • Ability to manipulate equations involving π and time variables
NEXT STEPS
  • Study the principles of uniform circular motion in detail
  • Learn how to derive kinematic equations for circular motion
  • Explore the concept of instantaneous vs. average acceleration
  • Investigate the effects of varying radius and time on acceleration calculations
USEFUL FOR

Physics students, educators, and anyone interested in the dynamics of circular motion and acceleration calculations.

LD_90
Messages
11
Reaction score
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.
 
Physics news on Phys.org
looks fine to me.
 
Thanks for the help.
 

Similar threads

Replies
55
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
16
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 16 ·
Replies
16
Views
11K
  • · Replies 5 ·
Replies
5
Views
5K
Replies
8
Views
1K
  • · Replies 11 ·
Replies
11
Views
2K
Replies
2
Views
2K