Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A point on the rim of a $0.75 m$ -diameter grinding wheel changes speed at a constant rate from $12 m/s$ to $25 m/s$ in $6.2 s$ . What is the average angular acceleration of the wheel?

Angular acceleration of the wheel is $5.60 rad / s^{2}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

i) Diameter of rim is $0.75 m$

ii) Initial speed is $12 m / s$

iii) Final speed is $25 m / s$

iv) Time period is $6.2 sec$

Step 2: Determining the concept

The rate of change of angular velocity of a body with respect to time is called angular acceleration. Find initial as well as final angular velocity using the relationship between rotational and linear velocity. Use a rotational kinematic equation to find the angular acceleration.

The angular velocity is given as-

$v = rω$

The angular acceleration is given as-

$α = \frac{Δω}{t}$

where, v is velocity, t is time, r is radius, $α$ is angular acceleration and $ω$ is angular frequency.

Step 3: Determining theangular acceleration of the wheel

Here, find the initial as well as final angular speed from the linear velocity as follows:

$v_{1} = r ω_{1}$

$12 m/s = (0.375 m) ω_{1}$

$ω_{1} = 32 rad/s$

$v_{2} = r ω_{2}$

$25 m/s = (0.375 m) ω_{2}$

$ω = 66.7 rad/s$

So, the change in angular speed is as follows:

$Δ ω = 66.7 rad/s - 32 rad/s$

$Δ ω = 34.7 rad/s$

Now, angular acceleration is as follows:

$α = \frac{Δ ω}{t}$

$α = \frac{34.7 rad/s}{6.2 s}$

$α = 5.60 rad/s$

Hence, angular acceleration of the wheel is $5.60 rad / s^{2}$ .

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Fundamentals Of Physics

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Short Answer

A point on the rim of a $0.75 m$ -diameter grinding wheel changes speed at a constant rate from $12 m/s$ to $25 m/s$ in $6.2 s$ . What is the average angular acceleration of the wheel?

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: Determining theangular acceleration of the wheel

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A point on the rim of a 0.75 m-diameter grinding wheel changes speed at a constant rate from 12 m/s to25 m/s in 6.2 s. What is the average angular acceleration of the wheel?

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: Determining theangular acceleration of the wheel

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A point on the rim of a $0.75 m$ -diameter grinding wheel changes speed at a constant rate from $12 m/s$ to $25 m/s$ in $6.2 s$ . What is the average angular acceleration of the wheel?