Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

A disk 8.00 cm in radius rotates at a constant rate of 1200 rev / min about its central axis. Determine (a) its angular speed in radians per second, (b) the tangential speed at a point 3.00 cm from its center, (c) the radial acceleration of a point on the rim, and (d) the total distance a point on the rim moves in 2.00 s.

The angular speed in radians per second of a disk is $ω_{i} = 126 r a d / s$
The tangential speed at a pointfrom its center is $v = 3.78 m / s$ .
The radial acceleration of a point on a rim is $a_{r} = 1270 m / s^{2}$ directed towards the centre.
The total distance a point on the rim moves in 2.00s is $d = 20.2 m$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The tangential speed formula

The tangential speed can be expressed in terms of angular speed, $v = ω r$ $ω$

is the angular speed, r is the radius.

Step 2: Calculation of the angular speed of a disk

(a)

To find the angular speed in radians per second, use the conversion factor,

Convert the unit from $(r e v / \min) t o (r a d / s) :$

$ω_{i} = 1200 (\frac{r e x}{m i x}) (\frac{2 π r a d}{1 r e x}) (\frac{1 \min}{60 s}) = 126 r a d / s$

Therefore, the angular speed is $ω_{i} = 126 r a d / s$

Step 3: The tangential speed

(b)

The formula for tangential speed is,

$v = ω r$

Since, the point is in 3.00 cm distance, r = 0.03 m

Substitute the values,

$ω = 126 r a d / s, r = 0.03 m$

Therefore,

$v = (126) (0.03) = 3.78 m / s$

Therefore, the tangential speed of a disk at a point 3.00 cm is $v = 3.78 m / s$ .

Step 4: Determination of the radial acceleration on a rim

(c)

Since, the radial acceleration can be expressed in terms of angular speed; the formula is given by,

$a_{r} = \frac{v^{2}}{r} = ω^{2} r$

Substitute the values, $ω = 126 r a d / s, r = 0.08 m$

$a_{r} = (126)^{2} (0.08) = 1270 m / s^{2}$

Therefore, the radial acceleration on a rim is $a_{r} = 1270 m / s^{2}$ directed towards the centre.

Step 5: Calculation of the total distance moved by the rim in 2s:

(d)

The formula for the total distance is,

$d = ω r t$

Substitute the given values,

$ω = 126 r a d / s, r = 0.08 m t = 2 s$

Therefore,

$d = (0.08) (126) (2) = 20.2 m$

Thus, the total distance moved by the rim in 2s is d=20.2m.

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: The tangential speed formula

Step 2: Calculation of the angular speed of a disk

Step 3: The tangential speed

Step 4: Determination of the radial acceleration on a rim

Step 5: Calculation of the total distance moved by the rim in 2s:

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: The tangential speed formula

Step 2: Calculation of the angular speed of a disk

Step 3: The tangential speed

Step 4: Determination of the radial acceleration on a rim

Step 5: Calculation of the total distance moved by the rim in 2s:

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