Understanding Relative Motion in Circular Motion

Click For Summary

Discussion Overview

The discussion revolves around understanding relative motion in circular motion, specifically focusing on the acceleration of one object relative to another in a circular path. Participants explore the concepts of tangential and radial acceleration in the context of a homework problem.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants present the equation for relative acceleration as a_A/B = a_A - a_B, with specific values for a_A and a_B given in terms of angular velocity and radius.
  • There is confusion about the direction of the acceleration vectors for objects A and B, with some participants questioning the correctness of their expressions.
  • Participants discuss whether the acceleration should be tangential or radial, with some asserting it should be tangential due to constant radius, while others argue it should only have radial acceleration.
  • One participant clarifies that the radial acceleration for B points from point B to point O, and for A, it points from point A to point O.
  • A later reply confirms the correct relative acceleration after considering the radial directions of the accelerations for A and B.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the nature of the acceleration (tangential vs. radial) and the correctness of their initial expressions. The discussion evolves as participants refine their understanding, but no consensus is reached on the initial interpretations.

Contextual Notes

Participants rely on specific assumptions about the motion being circular and the constancy of angular velocity, which may not be explicitly stated. The discussion also reflects uncertainty in the application of vector directions in the context of relative motion.

nysnacc
Messages
184
Reaction score
3

Homework Statement


13.164.png


Homework Equations


a= omega^2*r

The Attempt at a Solution


a_A/B = a_A - a_B

a_A = 10^2*r (-î)
a_B = 10^2*r (+ĵ)

a_A/B = 10^2*r (-î) - 10^2*r (+ĵ)
=> -200 î -200 ĵ

why is the answer 200 î -200 ĵ (accelerate in +î direction) ?
 
Physics news on Phys.org
nysnacc said:

Homework Statement


View attachment 105735

Homework Equations


a= omega^2*r

The Attempt at a Solution


a_A/B = a_A - a_B

a_A = 10^2*r (-î)
a_B = 10^2*r (+ĵ)

a_A/B = 10^2*r (-î) - 10^2*r (+ĵ)
=> -200 î -200 ĵ

why is the answer 200 î -200 ĵ (accelerate in +î direction) ?
The question is asking for the acceleration of A relative to B. What's the acceleration at A and at B independently?

Hint: Check the direction of acceleration vectors.
 
Last edited:
Student100 said:
The question is asking for the acceleration of A relative to B. What's the acceleration at A and at B independently?

Hint: Check the direction of acceleration vectors.

Err... isn't my expression correct..?

a_A = 10^2*r (-î). A is going -x, -y direction
a_B = 10^2*r (+ĵ). B is going -x, +y direction
 
nysnacc said:
Err... isn't my expression correct..?

a_A = 10^2*r (-î). A is going -x, -y direction
a_B = 10^2*r (+ĵ). B is going -x, +y direction

No. Should your acceleration be tangential or radial to the disk? Remeber the disk has constant angular velocity.
 
Student100 said:
No. Should your acceleration be tangential or radial to the disk? Remeber the disk has constant angular velocity.
should be tangential because constant radius??
 
nysnacc said:
should be tangential because constant radius??

Actually it should only have radial acceleration. Can you see why?
 
because constant rotation?
 
so the a_r for B is pointing from point B to Point O
and for A it is pointing from Point A to Point O?
 
nysnacc said:
so the a_r for B is pointing from point B to Point O
and for A it is pointing from Point A to Point O?

Exactly, so what's your relative acceleration now?
 
  • #10

so the a_r for B is omega^2*r (-i)
a_r for A is omega^2*r (-j)

a_A/B = a_A - a_B = -omega^2*r (j) - -omega^2*r (i)
rearrange = omega^2*r (i) - omega^2*r (j)

Got it! Thanks!
 

Similar threads

Engineering How do I know that the angular acceleration is the same for both wheels?
  • · Replies 19 ·
Replies
19
Views
3K
Find Magnitude & Direction for acceleration:
  • · Replies 1 ·
Replies
1
Views
3K
Which block reaches the wall faster?
  • · Replies 2 ·
Replies
2
Views
1K
Find Magnitude & Direction for acceleration
  • · Replies 12 ·
Replies
12
Views
5K
Relative motion between cars with different types of movements
  • · Replies 10 ·
Replies
10
Views
2K
Rigid body relative acceleration
  • · Replies 5 ·
Replies
5
Views
3K
Engineering Intro to Power Systems: Calculating Power
  • · Replies 7 ·
Replies
7
Views
2K
Comp Sci Optimal code for the array problem
  • · Replies 21 ·
Replies
21
Views
3K
Acc. of a drum joined to another drum with metal tape
  • · Replies 1 ·
Replies
1
Views
1K
Engineering An electric bulb of 500 W at 100v is used in a circuit
  • · Replies 7 ·
Replies
7
Views
2K