## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 5 - Problems - Page 186: 17

#### Answer

The dimensions for all three expressions are $[L][T]^{-2}$ which are the correct dimensions for acceleration.

#### Work Step by Step

The units for acceleration are $m/s^2$ Therefore, the dimensions for acceleration are $[L][T]^{-2}$, where $[L]$ is length and $[T]$ is time. The dimensions for velocity are $[L][T]^{-1}$ The dimensions for angular velocity are $[T]^{-1}$ The dimensions for radius are $[L]$ We can verify the dimensions of the three expressions for radial acceleration: The dimensions for $v\omega$ are $[L][T]^{-1}[T]^{-1} = [L][T]^{-2}$ The dimensions for $\frac{v^2}{r}$ are $\frac{[L]^2[T]^{-2}}{[L]} = [L][T]^{-2}$ The dimensions for $\omega^2~r$ are $[T]^{-2}[L] = [L][T]^{-2}$ The dimensions for all three expressions are $[L][T]^{-2}$ which are the correct dimensions for acceleration.

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