PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 5, Problem 12P
To determine

Rank the flywheels in order of the linear speed at the rim, largest to smallest.

Expert Solution & Answer
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Answer to Problem 12P

Since linear speed at the rim is directly proportional to radius/period, Ranking of the flywheels in order of the speed at the rim, from largest to smallest is (c)>(a)=(d)>(b)>(e).

Explanation of Solution

Write the expression for the linear speed.

v=ωr (I)

Here, v is the linear speed, ω is the angular velocity and r is the radius of spinning object.

Write the expression for the angular velocity.

ω=2πT

Here, T is the time period of rotation.

Substitute 2πT for ω in equation (I) to get v.

v=2πTr (II)

Consider option (a)

Radius of flywheel is 8.0cm and period is 4.0ms.

Substitute 8.0cm for r and 4.0ms for T in equation(II) to get v.

v=2π(4.0ms×1s103ms)cm(8.0cm×1m100)=40πm/s

Therefore, linear velocity flywheel is 40πm/s

Consider option (b)

Radius of flywheel is 2.0cm and period is 4.0ms.

v=2πTr (II)

Substitute 2.0cm for r and 4.0ms for T in equation(II) to get v.

v=2π(4.0ms×1s103ms)cm(2.0cm×1m100)=10πm/s

Therefore, linear velocity flywheel is 10πm/s

Consider option (c)

Radius of flywheel is 8.0cm and period is 1.0ms.

v=2πTr (II)

Substitute 8.0cm for r and 1.0ms for T in equation(II) to get v.

v=2π(1.0ms×1s103ms)cm(8.0cm×1m100)=160πm/s

Therefore, linear velocity flywheel is 160πm/s

Consider option (d)

Radius of flywheel is 2.0cm and period is 1.0ms.

v=2πTr (II)

Substitute 2.0cm for r and 1.0ms for T in equation(II) to get v.

v=2π(1.0ms×1s103ms)cm(2.0cm×1m100)=40πm/s

Therefore, linear velocity flywheel is 40πm/s

Consider option (e)

Radius of flywheel is 2.0cm and period is 1.0ms.

v=2πTr (II)

Substitute 1.0cm for r and 4.0ms for T in equation(II) to get v.

v=2π(4.0ms×1s103ms)cm(1.0cm×1m100)=5πm/s

Therefore, linear velocity flywheel is 5πm/s

Conclusion:

The above calculations indicates that flywheel given in option (c)and finally flywheel in option (e)has least velocity.

Since linear speed at the rim is directly proportional to radius/period, Ranking of the flywheels in order of the speed at the rim, from largest to smallest is (c)>(a)=(d)>(b)>(e).

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