Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781337026345
Author: Katz
Publisher: Cengage
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Chapter 12, Problem 60PQ

(a)

To determine

The average angular velocity of the pin wheel if it rotates from θ=0° to θ=180° in a time of 0.150s.

(a)

Expert Solution
Check Mark

Answer to Problem 60PQ

The average angular velocity of the pin wheel if it rotates from θ=0° to θ=90° in a time of 0.150s is 10.5rad/s_.

Explanation of Solution

Given that the pin wheel rotates from θ=0° to θ=90° in a time of 0.150s.

Write the expression for the average angular velocity of the pin wheel.

  ωav=ΔθΔt                                                                                                                   (I)

Here, ωav is the average angular velocity, and Δθ is the angular displacement, and Δt is the time duration.

Write the expression for the angular displacement of the pin wheel.

  Δθ=θfθi                                                                                                              (II)

Here, θf is the final angular distance, and θi is the initial angular distance.

Use equation (II) in (I).

  ωav=θfθiΔt                                                                                                            (III)

Conclusion:

Substitute 90° for θf, 0° for θi, and 0.150s for Δt in equation (III) to find the average angular velocity of the pin wheel ωav.

  ωav=90°0°0.150s=(90°0°)×2πrad360°0.150s=10.5rad/s

Therefore, the average angular velocity of the pin wheel if it rotates from θ=0° to θ=90° in a time of 0.150s is 10.5rad/s_.

(b)

To determine

The average angular velocity of the pin wheel if it rotates from θ=0° to θ=180° in a time of 0.300s.

(b)

Expert Solution
Check Mark

Answer to Problem 60PQ

The average angular velocity of the pin wheel if it rotates from θ=0° to θ=180° in a time of 0.300s is 10.5rad/s_.

Explanation of Solution

Given that the pin wheel rotates from θ=0° to θ=180° in a time of 0.300s.

Equation (III) gives the average angular velocity of the pin wheel.

  ωav=θfθiΔt

Conclusion:

Substitute 180° for θf, 0° for θi, and 0.300s for Δt in equation (III) to find the average angular velocity of the pin wheel ωav.

  ωav=180°0°0.300s=(180°0°)×2πrad360°0.300s=10.5rad/s

Therefore, the average angular velocity of the pin wheel if it rotates from θ=0° to θ=180° in a time of 0.300s is 10.5rad/s_.

(c)

To determine

The average angular velocity of the pin wheel if it rotates from θ=0° to θ=270° in a time of 0.450s.

(c)

Expert Solution
Check Mark

Answer to Problem 60PQ

The average angular velocity of the pin wheel if it rotates from θ=0° to θ=270° in a time of 0.450s is 10.5rad/s_ or 3.5rad/s_.

Explanation of Solution

Given that the pin wheel rotates from θ=0° to θ=270° in a time of 0.450s.

Equation (III) gives the average angular velocity of the pin wheel.

  ωav=θfθiΔt

Conclusion:

Substitute 270° for θf, 0° for θi, and 0.450s for Δt in equation (III) to find the average angular velocity of the pin wheel ωav.

  ωav=270°0°0.450s=(270°0°)×2πrad360°0.450s=10.5rad/s

Since the direction in which the pin wheel rotates is not mentioned, the net displacement corresponding to 270° is equivalent to a net angular displacement corresponding to 90° clockwise rotation (90°). Hence, substituting 90° for θf, 0° for θi, and 0.450s for Δt in equation (III) yields,

  ωav=90°0°0.450s=(90°0°)×2πrad360°0.450s=3.5rad/s

Therefore, the average angular velocity of the pin wheel if it rotates from θ=0° to θ=270° in a time of 0.450s is 10.5rad/s_ or 3.5rad/s_.

(d)

To determine

The average angular velocity of the pin wheel if it rotates from θ=0° through one revolution to θ=360° in a time of 0.600s.

(d)

Expert Solution
Check Mark

Answer to Problem 60PQ

The average angular velocity of the pin wheel if it rotates from θ=0° through one revolution to θ=360° in a time of 0.600s is 0rad/s_.

Explanation of Solution

Given that the pin wheel from θ=0° through one revolution to θ=360° in a time of 0.600s

Equation (III) gives the average angular velocity of the pin wheel.

Equation (I) gives the average angular velocity of the pin wheel.

  ωav=ΔθΔt

Conclusion:

During one revolution, the pin wheel covers 360° and reaches the same point from which it started its rotation, that is 0°. Since the final position and the initial position of the pin wheel’s rotation, the angular displacement is zero (Δθ=0). This leads equation (I) to yield the average angular velocity of the pinwheel to be zero.

  ωav=0rad0.600s=0rad/s

Therefore, the average angular velocity of the pin wheel if it rotates from θ=0° through one revolution to θ=360° in a time of 0.600s is 0rad/s_.

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Chapter 12 Solutions

Physics for Scientists and Engineers: Foundations and Connections

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