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Chapter 1: Problem 72

Write the unit of angular acceleration in the SI system. (a) \(\mathrm{N} \cdot \mathrm{Kg}\) (b) \(\mathrm{rad} /(\mathrm{sec})^{2}\) (c) \(\mathrm{m} / \mathrm{sec}\) (d) \(\mathrm{N} / \mathrm{kg}\)

Short Answer

Expert verified
The correct SI unit for angular acceleration is (b) \(\mathrm{rad} /(\mathrm{sec})^{2}\).

Step by step solution

01

Recall the definition of angular acceleration

Angular acceleration is the rate of change of angular velocity with respect to time. Mathematically, it can be written as: \[α = \frac{dω}{dt}\] Where \(α\) is the angular acceleration, \(ω\) is the angular velocity, and \(t\) is the time.
02

Identify the units for angular velocity and time

In the SI system, angular velocity is measured in radians per second (\(\mathrm{rad} / \mathrm{sec}\)), and time is measured in seconds (\(\mathrm{sec}\)).
03

Determine the unit for angular acceleration

Now that we know the units for angular velocity and time, we can determine the unit for angular acceleration (\(α\)). Since \(α = \frac{dω}{dt}\), the unit for angular acceleration is the units of angular velocity divided by the units of time. Therefore, we have: \[\mathrm{Unit\,for\,angular\,acceleration} = \frac{\mathrm{rad} / \mathrm{sec}}{\mathrm{sec}} = \mathrm{rad} /(\mathrm{sec})^{2}\]
04

Compare the result with the given options

Now, we can compare the derived unit for angular acceleration with the options provided in the exercise. The correct SI unit for angular acceleration is: \(\mathrm{rad} /(\mathrm{sec})^{2}\) Looking at the options, we see that this unit corresponds to: (b) \(\mathrm{rad} /(\mathrm{sec})^{2}\) So, the correct answer is (b).

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Most popular questions from this chapter

Write the dimensional formula of r.m.s (root mean square) speed. (a) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}\) (b) \(\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\) (c) \(\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}\) (d) \(\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-1}\)

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