What is the magnitude of acceleration of the ball? **Problem 5/125**The disk rotates with an angular speed \(\omega = 2 \, \text{rad/s}\). The small ball \(A\) is moving along the radial slot with a speed \(u = 100 \, \text{mm/s}\) relative to the disk. Determine the absolute velocity of the ball and state the angle \(\beta\) between this velocity vector and the positive \(x\)-axis.**Diagram Description:**- The diagram shows a disk with a radial slot. A small ball \(A\) is positioned on this slot.- The disk is rotating with angular speed \(\omega\) in the plane, indicated by a circular arrow.- The position of ball \(A\) is 125 mm from the center of the disk at point \(B\).- The disk has a reference \(xy\)-coordinate system overlaid, showing the orientation.- Vector \(u\) represents the speed of ball \(A\) relative to the disk, positioned along the radial slot towards the \(x\)-axis. The goal is to calculate the absolute velocity of the ball as it moves radially, and to find the angle \(\beta\) between this velocity vector and the positive \(x\)-axis.

Given: The angular speed is 2 rad/s. The speed of the ball is 100 mm/s. Consider the figure,

5/125 The disk rotates with angular speed -2 rad/s. The small ball A is moving along the radial slot with speed L= 100 mm/s relative to the disk. Determine the absolute velocity of the ball and state the angle B between this veloc- ity vector and the positive x-axis. 125 mm

5/125 The disk rotates with angular speed -2 rad/s. The small ball A is moving along the radial slot with speed L= 100 mm/s relative to the disk. Determine the absolute velocity of the ball and state the angle B between this veloc- ity vector and the positive x-axis. 125 mm

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

What is the magnitude of acceleration of the ball?

**Problem 5/125**

The disk rotates with an angular speed \(\omega = 2 \, \text{rad/s}\). The small ball \(A\) is moving along the radial slot with a speed \(u = 100 \, \text{mm/s}\) relative to the disk. Determine the absolute velocity of the ball and state the angle \(\beta\) between this velocity vector and the positive \(x\)-axis.

**Diagram Description:**
- The diagram shows a disk with a radial slot. A small ball \(A\) is positioned on this slot.
- The disk is rotating with angular speed \(\omega\) in the plane, indicated by a circular arrow.
- The position of ball \(A\) is 125 mm from the center of the disk at point \(B\).
- The disk has a reference \(xy\)-coordinate system overlaid, showing the orientation.
- Vector \(u\) represents the speed of ball \(A\) relative to the disk, positioned along the radial slot towards the \(x\)-axis.

The goal is to calculate the absolute velocity of the ball as it moves radially, and to find the angle \(\beta\) between this velocity vector and the positive \(x\)-axis.

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