# Relative Motion using Rotatin Axis

## 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.

#### Attachments

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## Answers and Replies

Chi Meson
Science Advisor
Homework Helper
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)