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Relative Motion using Rotatin Axis

  • Thread starter joemama69
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  • #1
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Homework Statement


While the bridge is closing with a constant rotation of .5 rad/s, a man runs along the roadway such that when d=10ft, he is running outward from the center at 5 ft/s with an acceleration of 2 ft/s^2, both measured relative to the roadway. Determine his velocity and acceleration at this instant.


Homework Equations



V(a) = V(o) + Omega X r(a/o) + v(a/o)
A(a) = A(o) + Omega' X r(a/o) + Omega X (Omega X r(a/o)) + 2Omega X V(a/o) + A(a/o)


The Attempt at a Solution



V(o) = 0, Omega = .5k, Omega' = 0, r(a/o) = 10j, V(a/o) = -5j, A(a/o) = -2j

Lets do velocity first

Omega X r(a/o) = -5i

V(a) = 0 + -5i + -5j = -5i - 5j ft/s


Now Acceleration

Omega' X r(a/o) = 0
Omega X (Omega X r(a/o)) = 2.5j
2Omega X v(a/o) = 5j

A(a) = 0 + 0 + 2.5j + 5j + -2j = 5.5j ft/s^2


Shouldn't the velocity and acceleration be in the same direction.
 

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Answers and Replies

  • #2
Chi Meson
Science Advisor
Homework Helper
1,789
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Shouldn't the velocity and acceleration be in the same direction.
No, they rarely are in the same direction. Think about circular motion: what's the direction of the tangential velocity, and what is the direction of centripetal acceleration? (the names give away the answer)
 

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