Log out Go to App
Go to App

Learning Materials

Features

Discover

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).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Which physical quantity has unit of pascal - second? (a) Velocity (b) viscosity (c) energy (d) coefficient of viscosity

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) \(\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-1}\)

Dimensional formula for torque is (a) \(\mathrm{M}^{2} \mathrm{~L}^{2} \mathrm{~T}^{-3}\) (b) \(\mathrm{M}^{2} \mathrm{~L}^{1} \mathrm{~T}^{-2}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\) (d) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}\)

\( 1 \mathrm{Mev}=\ldots \ldots \ldots \ldots \ldots\) (a) \(10^{7}\) (b) \(10^{4}\) (c) \(10^{5}\) (d) \(10^{6}\)

Dimensional formula for thermal conductivity (k) is.. (a) \(\mathrm{M}^{2} \mathrm{~L}^{1} \mathrm{~T}^{-2} \mathrm{~K}^{-1}\) (b) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2} \mathrm{~K}^{1}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-3} \mathrm{~K}^{-1}\) (d) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~K}^{-1}\)
See all solutions

Recommended explanations on English Textbooks

Pragmatics

Read Explanation

Cues and Conventions

Read Explanation

Listening and Speaking

Read Explanation

Free Response Essay

Read Explanation

English Grammar

Read Explanation

Creative Story

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free