A motorized wheel is spinning with a rotational velocity of \( \omega_0 = 1.81 \, \text{rad/s} \). At \( t = 0 \, \text{s} \), the operator switches the wheel to a higher speed setting. The rotational velocity of the wheel at all subsequent times is given by:\[\omega(t) = \omega_0 \arctan (c + bt^2)\]where \( c = 1.5574 \) and \( b = 6.09 \, \text{s}^{-2} \).**Questions and Answers:**1. **At what time \( t_{\text{max}} \) is the rotational acceleration at a maximum?** **Answer Provided:** \( t_{\text{max}} = 0.358 \, \text{ms} \) **Status:** Incorrect2. **What is the maximum tangential acceleration \( a_t \) of a point on the wheel a distance \( R = 1.29 \, \text{m} \) from its center?** **Answer Provided:** \( a_t = 0.126 \, \text{m/s}^2 \) **Status:** Incorrect3. **What is the magnitude of the total acceleration of this point?** **Answer Provided:** \( a = 239.4 \, \text{m/s}^2 \) **Status:** Incorrect**Note:** The provided answers are flagged as incorrect, indicating a need for review or recalculation to find the correct solutions.

A motorized wheel is spinning with a rotational velocity of wo = 1.81 rad/s. At t = 0s, the operator switches the wheel to a higher speed setting. The rotational velocity of the wheel at all subsequent times is given by w (t) = woarctan (c + bt²) where c = 1.5574 and b = 6.09 S-2 At what time tamax is the rotational acceleration at a maximum? tamax a₁ = What is the maximum tangential acceleration a, of a point on the wheel a distance R = 1.29 m from its center? 0.358 Incorrect a 0.126 Incorrect What is the magnitude of the total acceleration of this point? 239.4 Incorrect Attem m/s² ms m/s2

A motorized wheel is spinning with a rotational velocity of wo = 1.81 rad/s. At t = 0s, the operator switches the wheel to a higher speed setting. The rotational velocity of the wheel at all subsequent times is given by w (t) = woarctan (c + bt²) where c = 1.5574 and b = 6.09 S-2 At what time tamax is the rotational acceleration at a maximum? tamax a₁ = What is the maximum tangential acceleration a, of a point on the wheel a distance R = 1.29 m from its center? 0.358 Incorrect a 0.126 Incorrect What is the magnitude of the total acceleration of this point? 239.4 Incorrect Attem m/s² ms m/s2

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

A motorized wheel is spinning with a rotational velocity of \( \omega_0 = 1.81 \, \text{rad/s} \). At \( t = 0 \, \text{s} \), the operator switches the wheel to a higher speed setting. The rotational velocity of the wheel at all subsequent times is given by:

\[
\omega(t) = \omega_0 \arctan (c + bt^2)
\]

where \( c = 1.5574 \) and \( b = 6.09 \, \text{s}^{-2} \).

**Questions and Answers:**

1. **At what time \( t_{\text{max}} \) is the rotational acceleration at a maximum?**

**Answer Provided:** \( t_{\text{max}} = 0.358 \, \text{ms} \)
**Status:** Incorrect

2. **What is the maximum tangential acceleration \( a_t \) of a point on the wheel a distance \( R = 1.29 \, \text{m} \) from its center?**

**Answer Provided:** \( a_t = 0.126 \, \text{m/s}^2 \)
**Status:** Incorrect

3. **What is the magnitude of the total acceleration of this point?**

**Answer Provided:** \( a = 239.4 \, \text{m/s}^2 \)
**Status:** Incorrect

**Note:** The provided answers are flagged as incorrect, indicating a need for review or recalculation to find the correct solutions.

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