Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 5, Problem 13P
To determine

The ranking of the flywheels in descending order of the radial acceleration of a point on the rim.

Expert Solution & Answer
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Answer to Problem 13P

The ranking of the flywheels in descending order of the radial acceleration of a point on the rim is (c),(d),(a),(b),(e) .

Explanation of Solution

Write the expression for the radial acceleration.

ar=ω2r (I)

Here, ar is the radial acceleration, w is the angular velocity and r is the radius

Write the expression for the angular velocity.

ω=2πT

Here, T is the period of the motion

Put the above equation in equation (I).

ar=(2πT)2rar=4π2rT2arrT2 (II)

Conclusion:

Find the values of (rT2) for the different flywheels.

(a)

Given that the radius of the wheel is 8.0 cm and the period is 4.0 ms .

Substitute 8.0 cm for r and 4.0 ms for T in expression (II) to find ar .

ar8.0 cm(1 m100 cm)(4.0 ms(1 s1000 ms))2=0.08 m(0.004 s)2=5000 m/s2

(b)

Given that the radius of the wheel is 2.0 cm and the period is 4.0 ms .

Substitute 2.0 cm for r and 4.0 ms for T in expression (II) to find ar .

ar2.0 cm(1 m100 cm)(4.0 ms(1 s1000 ms))2=0.02 m(0.004 s)2=1250 m/s2

(c)

Given that the radius of the wheel is 8.0 cm and the period is 1.0 ms .

Substitute 8.0 cm for r and 1.0 ms for T in expression (II) to find ar .

ar8.0 cm(1 m100 cm)(1.0 ms(1 s1000 ms))2=0.08 m(0.001 s)2=80000 m/s2

(d)

Given that the radius of the wheel is 2.0 cm and the period is 1.0 ms .

Substitute 2.0 cm for r and 1.0 ms for T in expression (II) to find ar .

ar2.0 cm(1 m100 cm)(1.0 ms(1 s1000 ms))2=0.02 m(0.001 s)2=20000 m/s2

(e)

Given that the radius of the wheel is 1.0 cm and the period is 4.0 ms .

Substitute 1.0 cm for r and 4.0 ms for T in expression (II) to find ar .

ar1.0 cm(1 m100 cm)(4.0 ms(1 s1000 ms))2=0.01 m(0.004 s)2=625 m/s2

Therefore, the ranking of the flywheels in descending order of the radial acceleration of a point on the rim is (c),(d),(a),(b),(e) .

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Chapter 5 Solutions

Physics

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