COLLEGE PHYSICS-CONNECT ACCESS
COLLEGE PHYSICS-CONNECT ACCESS
5th Edition
ISBN: 9781260486834
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 5, Problem 53P

(a)

To determine

The time taken by the rotor to spin before coming to rest.

(a)

Expert Solution
Check Mark

Answer to Problem 53P

The time taken by the rotor to spin before coming to rest is 12.5×105s_.

Explanation of Solution

Write the relation between angular speed and angular acceleration.

    ωfωi=αΔt

Here, ωf is the final angular speed, ωi is the initial angular speed, α is the angular acceleration, and Δt is the time taken by the rotor to spin.

Since the final angular speed of the rotor is zero and the rotor is slowing down at an angular acceleration of α the above equation is reduced to

    0ωi=αΔt

Rearrange the above equation to find Δt.

    Δt=ωiα        (I)

Conclusion:

Substitute 5×105rad/s for ωi, and 0.4rad/s2 for α in equation (I), to find Δt.

    Δt=5×105rad/s(0.4rad/s2)=1250000s=12.5×105s

Therefore, the time taken by the rotor to spin before coming to rest is 12.5×105s_.

(b)

To determine

The angular displacement of the rotor during the time interval Δt.

(b)

Expert Solution
Check Mark

Answer to Problem 53P

The angular displacement of the rotor during the time interval Δt is 5×1010rev_.

Explanation of Solution

Write the expression for angular displacement Δθ.

    Δθ=ωiΔt+12α(Δt)2        (II)

Here, Δθ is the angular displacement, ωi is the initial angular speed, Δt is the time taken to rotate, and α is the angular acceleration.

Write the expression for number of revolution of the rotor.

    The number of revolution =Δθ2πrad/s        (III)

Conclusion:

Substitute 12.5×105s for Δt, 5×105rad/s for ωi, and 0.4rad/s2 for α in equation (II), to find Δθ.

    Δθ=(5×105rad/s)(12.5×105s)+12(0.4rad/s2)(12.5×105s)2=6.25×1011rad3.125×1011rad=3.125×1011rad

Substitute 3.125×1011rad for Δθ in equation (III), to find the number of revolutions.

    The number of revolution =3.125×1011rad2(3.14)rad/rev=4.97×1010rev5×1010rev

Therefore, the angular displacement of the rotor during the time interval Δt is 5×1010rev_.

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Chapter 5 Solutions

COLLEGE PHYSICS-CONNECT ACCESS

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