**Transcription for Educational Website:****Figure 9.1:**[Diagram Description]The diagram shows a wheel with a radius of 2.0 meters, centered at point O. The wheel rotates counterclockwise with an angular acceleration of $ \alpha = 0.01 \, \text{rad/s}^2 $. Point P is marked on the rim of the wheel, positioned initially along the x-axis.**Problem Statement:**Point P is on the rim of a wheel with a radius of 2.0 m. At time $ t = 0 $, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform angular acceleration of $ 0.01 \, \text{rad/s}^2 $ about the center O.In Figure 9.1, the magnitude of the linear acceleration of P, when it reaches the y-axis, is closest to:- A. $ 0.008 \, \text{m/s}^2 $- B. $ 0.064 \, \text{m/s}^2 $- C. $ 0.063 \, \text{m/s}^2 $- D. $ 0.075 \, \text{m/s}^2 $- E. $ 0.072 \, \text{m/s}^2 $**Analysis:**This question involves calculating the linear acceleration of a point on the rim of a wheel as it rotates under specified conditions. The linear acceleration can be determined by analyzing both tangential and centripetal components due to the wheel's motion.

radius = r = 2 m angular acceleration = α= 0.01 rad/s2 when it reaches the y- axis angular…

-0.01 rad/s2 2.0m oint Pis on the rim of a wheel of radius 2.0 m. At timet= 0, the wheel is at rest, and Pis on the x-a. The wheel undergoes a uniform angular acceleration of g.01 radis about the center o. Figure 8.1, the magnitude of the linear acceleration of P. when it reaches the y-axis, is dosest to: DÃ 0 000 mis? O B. 0.088 mis? OCo.083 mis? O D.0.075 mis? DE 0.072 mis?

-0.01 rad/s2 2.0m oint Pis on the rim of a wheel of radius 2.0 m. At timet= 0, the wheel is at rest, and Pis on the x-a. The wheel undergoes a uniform angular acceleration of g.01 radis about the center o. Figure 8.1, the magnitude of the linear acceleration of P. when it reaches the y-axis, is dosest to: DÃ 0 000 mis? O B. 0.088 mis? OCo.083 mis? O D.0.075 mis? DE 0.072 mis?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 62PQ: Problems 62 and 63 are paired. 62. C A disk is rotating around a fixed axis that passes through its...

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**Transcription for Educational Website:**

**Figure 9.1:**

[Diagram Description]
The diagram shows a wheel with a radius of 2.0 meters, centered at point O. The wheel rotates counterclockwise with an angular acceleration of $ \alpha = 0.01 \, \text{rad/s}^2 $. Point P is marked on the rim of the wheel, positioned initially along the x-axis.

**Problem Statement:**
Point P is on the rim of a wheel with a radius of 2.0 m. At time $ t = 0 $, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform angular acceleration of $ 0.01 \, \text{rad/s}^2 $ about the center O.

In Figure 9.1, the magnitude of the linear acceleration of P, when it reaches the y-axis, is closest to:
- A. $ 0.008 \, \text{m/s}^2 $
- B. $ 0.064 \, \text{m/s}^2 $
- C. $ 0.063 \, \text{m/s}^2 $
- D. $ 0.075 \, \text{m/s}^2 $
- E. $ 0.072 \, \text{m/s}^2 $

**Analysis:**
This question involves calculating the linear acceleration of a point on the rim of a wheel as it rotates under specified conditions. The linear acceleration can be determined by analyzing both tangential and centripetal components due to the wheel's motion.

Expert Solution

Step 1

radius = r = 2 m

angular acceleration = $α$ = 0.01 rad/s²

when it reaches the y- axis angular displacement= $θ$ = $\frac{π}{2}$ = $\frac{3.14}{2}$ =1.57 rad

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