Question 2. A uniform bar of mass m and length L is pivoted at point O, as shown in Figure 2 below. A point mass M is at

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Question 2 A Uniform Bar Of Mass M And Length L Is Pivoted At Point O As Shown In Figure 2 Below A Point Mass M Is At 1 (170.26 KiB) Viewed 19 times

Question 2. A uniform bar of mass m and length L is pivoted at point O, as shown in Figure 2 below. A point mass M is attached to the bar at a distance d from point 0. Part I. The bar is released from rest from the position shown. Immediately after the release: (a) Draw the free-body-diagram showing all the forces acting on the bar. [6 marks] [13 marks] (b) Obtain an expression for the angular acceleration of the bar in terms of m, M, L, d. g, and 8 (g is the acceleration due to gravity) in the fixed frame A (in terms of a unit vector). (c) Find the magnitude of d for which the angular acceleration maximises. [5 marks] Briefly explain the reasoning for your choice Part II. Now assume that the bar has an angular velocity wg as when passing through the position shown in Figure 2. For this system: (d) Does the angular acceleration of the bar change from the expression [3 marks] obtained in Part I(b)? Explain why. (e) How do the magnitudes of the reaction forces at O change compared to Part I? You do not need to obtain expressions for the forces; discuss [6 marks] whether each force is larger or smaller compared to that of the system of Part I and explain why. Total: [33 marks] āz Suggested time: 45 minutes. Figure 2 Page 5 of 8 8 d3 a₁ d M A