Kinetics of rigid bodies, Mechanical Engineering

Kinetics of Rigid Bodies:

For the bodies undergoing plane motion, a common scheme for solutions is to apply the equations of dynamic equilibrium as below.

∑ Fx  = m ax ,         ∑ Fy  = m a y

∑ M = I α

Keeping in mind that ax, ay and I are calculated with reference to centroidal axes. Inertia forces and inertia couple should be applied to the body before writing down these equilibrium equations. The relation between ax and α is normally obtained by using kinematic relationships.

When motion of rotation takes place about an axis which is not coinciding with centroidal axis, it is convenient to select x and y axis through the mass centre which are positive in the direction of an and ar, respectively. Also ∑ M A  - I A  α = 0 is the equation to be utilized which normally gets rid of the unknown reaction at the axle A. Then these equations get transformed into

∑ Fx = mr ω2

∑ Fy = mr α

∑ M = I α; ∑ M A = I A α

In case of centroidal rotation A coincides with mass centre, r = 0 and the above equations reduce to

∑ Fx  = 0,         ∑ Fy  = 0,           ∑ M = Iα

For homogeneous rolling bodies in which mass centre has a rectilinear motion parallel to the surface on which it rolls it is suitable to select reference axes at the mass centre with the x axis parallel to the surface and positive in the initial direction of motion. The equations become

∑ Fx = m a, ∑ Fy = 0, ∑ M = Iα

If the body rolls without slipping, an additional equation can be used

∑ M c = I c α

Posted Date: 1/29/2013 6:44:47 AM | Location : United States

Related Discussions:- Kinetics of rigid bodies, Assignment Help, Ask Question on Kinetics of rigid bodies, Get Answer, Expert's Help, Kinetics of rigid bodies Discussions

Write discussion on Kinetics of rigid bodies
Your posts are moderated
Related Questions
Illustrate various kinds of control systems. Illustrate several block diagram reduction rules with examples. Determine C/R by using block diagram reduction method.

explain wedge friction?with simple example? solve any simple problem in wedge friction

procedure/equation for welding of two dissimilar mterial in finate element method?

Are the types of pumps selected (base mounted, in-line)? Locate pump on discharge side of boiler. Flexible connector used. Valving indicated, isolation valve on suction and dis

law of belting

Hi. I have made a payment for the above ticket number. Will I get all the workings out too?

System of force

Objectives After studying this section, you should be capable to: define basic nature of plastics, differentiate between various types of plastics, define polym

how to flow chart Volume calculation ?

Clutch cable routing :Ensure that the cable is routed as per standard routing, through the brackets provided.