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Chapter 8: Problem 73

How long would a braking torque of \(4.00 \mathrm{N}\).m have to act to just stop a spinning wheel that has an initial angular momentum of $6.40 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s} ?$

Short Answer

Expert verified
Answer: The braking torque needs to act for 1.60 seconds to stop the spinning wheel.

Step by step solution

01

Identify the given values

In this exercise, we are given: - Braking Torque (T) = \(4.00 \mathrm{N} \cdot \mathrm{m}\) - Initial Angular Momentum (L_initial) = \(6.40 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}\)
02

Calculate the change in angular momentum

As the wheel must come to a complete halt, the final angular momentum will be zero. Hence, the change in angular momentum can be calculated as: Change in Angular Momentum (ΔL) = L_final - L_initial = \(0 - 6.40 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s} = -6.40 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}\)
03

Find the time required for braking torque to stop the wheel

Using the formula mentioned in the analysis, we can find the time required for the braking torque to stop the wheel. Rearrange the formula to find the time: Time (t) = Change in Angular Momentum / Torque Plug in the values: t = \(\frac{-6.40 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}}{4.00 \mathrm{N} \cdot \mathrm{m}}\) t = -1.60 s Since the time cannot be negative, we will take the absolute value: t = 1.60 s
04

Final Answer

The braking torque of \(4.00 \mathrm{N} \cdot \mathrm{m}\) must act for 1.60 seconds to stop the spinning wheel with an initial angular momentum of \(6.40 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}\).

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Most popular questions from this chapter

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