Understanding Relative Motion in Circular Motion

[nysnacc]

Homework Statement

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) ?

 

[Student100]

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.

 

[nysnacc]

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

 

[Student100]

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.

 

[nysnacc]

No. Should your acceleration be tangential or radial to the disk? Remeber the disk has constant angular velocity.

should be tangential because constant radius??

 

[Student100]

should be tangential because constant radius??

Actually it should only have radial acceleration. Can you see why?

 

[nysnacc]

because constant rotation?

 

[nysnacc]

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?

 

[Student100]

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?

 

[nysnacc]

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!