Understanding Relative Motion in Circular Motion

In summary: So the relative acceleration of A is going in the opposite direction as B. Exactly, so what's your relative acceleration now?
  • #1
nysnacc
184
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) ?
 
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  • #2
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:
  • #3
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
 
  • #4
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.
 
  • #5
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??
 
  • #6
nysnacc said:
should be tangential because constant radius??

Actually it should only have radial acceleration. Can you see why?
 
  • #7
because constant rotation?
 
  • #8
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?
 
  • #9
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!
 

Related to Understanding Relative Motion in Circular Motion

What is relative motion in a circle?

Relative motion in a circle refers to the motion of an object or point in a circular path with respect to another object or reference point. It is the perception of movement from the viewpoint of a moving observer.

What is the difference between absolute and relative motion?

Absolute motion is the actual movement of an object in space, while relative motion is the perceived movement of an object from the perspective of an observer. Absolute motion is measured with respect to a fixed point, while relative motion is measured with respect to another moving point.

How is relative motion in a circle calculated?

The relative motion in a circle can be calculated using the formula v = ωr, where v is the tangential velocity, ω is the angular velocity, and r is the radius of the circle. This formula relates the linear and angular velocities in a circular motion.

What is centripetal acceleration in relative motion?

Centripetal acceleration is the acceleration that an object experiences when moving in a circular path. In relative motion, it is the acceleration experienced by the object with respect to the moving observer. It is always directed towards the center of the circle.

What are some real-world examples of relative motion in a circle?

Some examples of relative motion in a circle include the motion of a car around a roundabout, the rotation of the Earth around the Sun, and the motion of a satellite orbiting around the Earth. These motions can be observed from a stationary reference point, such as the ground, and appear to be moving in a circular path.

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