The wheel has radius ?? = 60 cmand is free to rotate without friction about acentral axle. A force ?? = 15N is applied tothe wheel as shown, at distance ?? = 20 cm.from the axle. ?? = 50° The image depicts a circle with two radii labeled $ R $ and $ r $. The circle is placed within a coordinate system with horizontal and vertical axes labeled $ x $ and $ y $, respectively. - $ R $ represents the radius from the center of the circle to its edge.- $ r $ indicates the radius of a smaller circle or an inner circle from the same center.- An arrow is drawn from the center of the circle to a point on the circumference, forming an angle $ \phi $ with the horizontal baseline.- The angle $\phi$ is measured between the radius $ r $ and the x-axis.This diagram is likely used to illustrate concepts in polar coordinates, where $ \phi $ represents the angle from the reference direction, and $ r $ is the radial distance. **Problem:**With the wheel starting from rest, this torque is applied constantly. After three revolutions, its final angular speed is $ \omega_f = 8.0 \, \text{s}^{-1} $. What was its angular acceleration $ \alpha $?

Answered: c. With the wheel starting from rest,…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

The wheel has radius ?? = 60 cm
and is free to rotate without friction about a
central axle. A force ?? = 15N is applied to
the wheel as shown, at distance ?? = 20 cm.
from the axle. ?? = 50°

The image depicts a circle with two radii labeled $ R $ and $ r $. The circle is placed within a coordinate system with horizontal and vertical axes labeled $ x $ and $ y $, respectively.

- $ R $ represents the radius from the center of the circle to its edge.
- $ r $ indicates the radius of a smaller circle or an inner circle from the same center.
- An arrow is drawn from the center of the circle to a point on the circumference, forming an angle $ \phi $ with the horizontal baseline.
- The angle $\phi$ is measured between the radius $ r $ and the x-axis.

This diagram is likely used to illustrate concepts in polar coordinates, where $ \phi $ represents the angle from the reference direction, and $ r $ is the radial distance.

**Problem:**

With the wheel starting from rest, this torque is applied constantly. After three revolutions, its final angular speed is $ \omega_f = 8.0 \, \text{s}^{-1} $. What was its angular acceleration $ \alpha $?

Expert Solution

Step 1

The angular acceleration expression

$ω_{f}^{2} = ω_{i}^{2} + 2 α ∆ s ω_{f}^{2} = 0 + 2 α ∆ s \Rightarrow α = \frac{ω_{f}^{2}}{2 ∆ s}$

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