The disk has a constant angular velocity of 20 rad/s Clockwise. Note that the point A is hinged at a Axed location. + y A Idea WA = 40A dt 20 rad/s D £ 70mm A a) Determine the two values of the angle & for which the velocity of collar D is zero. WA dz fo b) For each of these values of 0, determine the Corresponding value of the angular velocity of bar BD. 250mm WA= 20 rad/s

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Problem Statement

The disk has a constant angular velocity of 20 rad/s clockwise. Note that the point A is hinged at a fixed location.

#### Given
- Angular velocity of disk, \( \omega_A = 20 \, \text{rad/s} \)

### Diagram Description

The diagram shows:
- A circular disk with center A, rotating clockwise.
- Point A is fixed.
- A bar extending from point A to a collar at point D, with a length of 250 mm.
- The collar is free to move along a vertical line.
- The horizontal line intersects the circle at a point that’s 70 mm from the top of the disk.
- \( x \) and \( y \) axes are shown for reference.

### Tasks

**(a)** Determine the two values of the angle \( \theta \) for which the velocity of collar D is zero.

**(b)** For each of these values of \( \theta \), determine the corresponding value of the angular velocity of bar BD.

### Given Equations

\[ \omega_A = \frac{d\theta_A}{dt} \]

\[ \int_{\theta_{A_0}}^{\theta} d\theta_A = \int_{t_0}^{t} \omega_A \, dt \]

### Solution Approach

- Find conditions where the velocity of point D is zero.
- Calculate angular velocities for bar BD based on those conditions.

This explanation and the figure are intended to aid in solving problems related to rotational motion and the interrelationship between fixed and moving parts in a mechanical system.
Transcribed Image Text:### Problem Statement The disk has a constant angular velocity of 20 rad/s clockwise. Note that the point A is hinged at a fixed location. #### Given - Angular velocity of disk, \( \omega_A = 20 \, \text{rad/s} \) ### Diagram Description The diagram shows: - A circular disk with center A, rotating clockwise. - Point A is fixed. - A bar extending from point A to a collar at point D, with a length of 250 mm. - The collar is free to move along a vertical line. - The horizontal line intersects the circle at a point that’s 70 mm from the top of the disk. - \( x \) and \( y \) axes are shown for reference. ### Tasks **(a)** Determine the two values of the angle \( \theta \) for which the velocity of collar D is zero. **(b)** For each of these values of \( \theta \), determine the corresponding value of the angular velocity of bar BD. ### Given Equations \[ \omega_A = \frac{d\theta_A}{dt} \] \[ \int_{\theta_{A_0}}^{\theta} d\theta_A = \int_{t_0}^{t} \omega_A \, dt \] ### Solution Approach - Find conditions where the velocity of point D is zero. - Calculate angular velocities for bar BD based on those conditions. This explanation and the figure are intended to aid in solving problems related to rotational motion and the interrelationship between fixed and moving parts in a mechanical system.
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