Determine the angular-velocity of uniform bar, Mechanical Engineering

Determine the angular-velocity of uniform bar:

A uniform bar of length l and mass M is hinged at its end B and is released from its horizontal position BA. Determine its angular-velocity at any angle θ with BA and at the instant while it is vertical where A2 is the lowest position of end A.

Solution

 The bar BA being of uniform size and mass has its weight (W) at its mid-point and it undergoes a motion of rotation about axis at B. Note that this axis of rotation is horizontal (i.e. perpendicular to the plane of the paper) since motion of rotation is in vertical plane.

When the bar takes any position BA1 at an ∠ θ, the C. G. of bar comes down vertically by (l/2) sin θ . Applying the principle of conservation of energy, letting the datum level as AB, since initial angular velocity in position BA is zero,

Initial total energy      = PE of (BA) + KE in position (BA)

                                     = 0

Total energy in position (BA1) = PE (BA1) + KE (BA1)

= - ( Mg(l/2) sin θ )+ (I (m)1)2 )/2

PE (BA1) is negative since its CG is below datum level and ω1 is angular velocity of the bar when A reaches A1.

As per the principle,

∴ I (m) (ω1)2  /2- Mg(l/2)sin θ = 0

Ml2/3× (ω1)2 /2 = Mg (l/2) sin θ

∴(ω1)2 = (3 g sin θ)/l

At lowest position BAL when θ = 90o.

L)2 = 3 g/l

Linear velocity of the lowest point AL is in horizontal direction and its magnitude is given by

1008_Determine the angular-velocity of uniform bar.png

Posted Date: 1/29/2013 7:22:30 AM | Location : United States







Related Discussions:- Determine the angular-velocity of uniform bar, Assignment Help, Ask Question on Determine the angular-velocity of uniform bar, Get Answer, Expert's Help, Determine the angular-velocity of uniform bar Discussions

Write discussion on Determine the angular-velocity of uniform bar
Your posts are moderated
Related Questions
Derive and expression for force exerted by a jet of water on fixed vertical plate in direction of

If Battery Discharges Frequently Causes of Problem Remedy Electrolyte specific gravity NG Charging not done fully

Load on beam: A beam AB as shown in the figure given below is hinged at A and supported at B by a vertical cord that passes over two frictionless pulleys C and

Calculate the Machining Time and the Material Removal Rate A through hole of 40 mm diameter and 50 mm depth is to be drilled in a mild steel component. The cutting speed can b

A piston-cylinder assembly fitted with a paddle wheel contains air, initially at p1=30 lbf/in2, T1=540 °F, and V1=4 ft3. The air undergoes a process to a final state where p2=20 lb

Q. Explain working of plate heat exchangers? For gasket plate heat exchangers handling flammable materials, the same spacing requirements for air coolers should be applied. If

Submerged Arc Welding   Single pass filler welds upto (8.0 mm) maximum and groove welds made with a single pass or a single pass each side, may be made using an E7os-x elect

How is metal removed in metal cutting ? Explain the process by giving simple model to explain the metal removed process. What are the different conditions that could allow a con

Windmills were traditionally used for processing grains, later they started to be used for electricity production as well. Windmills can also be used to pump water.

Effective communication is an itergral aspect in the mechanical engineering field, base on arguement