# The Similarities And Differences Of Kinetics Of A Rigid Body

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The similarities and differences of Kinetics of a Particle: Work and Energy and Planar Kinetics of a Rigid Body: Work and Energy. Kinetics of a particle: work and energy shows the particle moving when forces are applied to it and produces work and energy. Meanwhile under planar kinetics of a rigid body shows the rigid body on the plane when forces are applied and produces work and energy. There are similarities and differences between both of it. Kinetics of a particle Planar kinetics of a rigid body

Similarities - Conservation of energy

- Conservation forces and potential energy

*gravitational

*elastic/plastic

- Principle of work and kinetic energy

*T1+ƩU1-2=T2

Differences - The work of forces

*not constant forces

*have work if variable

Therefore, any problem that can be solved by the work-energy method can, in theory, be solved using the FMA method. There is main advantage of using work and energy method compared to the force-mass-acceleration (FMA) method.

1. Work can be calculated in problem without integration, the change in speed of the particle may be easily obtained with a minimum of computation.

2. Only forces that do work need to be considered which mean a nonworking force does not have to use.

3. If the final position is chosen to be an arbitrary position, the work and energy method will determine the speed as a function of a position of the particle.

In the rigid body, the forces internal to a rigid body hold the body together which the forces that imposed the condition of the rigidity is constrained. These internal forces occur in equal and opposite collinear pairs. Because the body is rigid, distances are not change between the particles, which in turn implies that the distances between the points of application of the internal forces remain constant. (U1-2)ext=ΔT

For example anywhere on the body, there are two parallel forces F acting in the plane of motion of a body. The forces are acting oppositely directions, and R is the perpendicular distance between these forces which are called force couple and they exert a moment on that body.

The moment of a force is anywhere this force couple is located relative to an arbitrary point O, they will always exert the same moment. The direction of the moment due to this couple is given by the right hand rule and it is perpendicular to the plane containing the force pair. The magnitude of the moment Mo caused by the force couple is given by:

If the body rotates in the plane between two angles α1 and α2, the work done by Mo on the body is given by

where α is measured in radians.

If Mo is constant

Similarities - Conservation of energy

- Conservation forces and potential energy

*gravitational

*elastic/plastic

- Principle of work and kinetic energy

*T1+ƩU1-2=T2

Differences - The work of forces

*not constant forces

*have work if variable

*…show more content…*Therefore, any problem that can be solved by the work-energy method can, in theory, be solved using the FMA method. There is main advantage of using work and energy method compared to the force-mass-acceleration (FMA) method.

1. Work can be calculated in problem without integration, the change in speed of the particle may be easily obtained with a minimum of computation.

2. Only forces that do work need to be considered which mean a nonworking force does not have to use.

3. If the final position is chosen to be an arbitrary position, the work and energy method will determine the speed as a function of a position of the particle.

In the rigid body, the forces internal to a rigid body hold the body together which the forces that imposed the condition of the rigidity is constrained. These internal forces occur in equal and opposite collinear pairs. Because the body is rigid, distances are not change between the particles, which in turn implies that the distances between the points of application of the internal forces remain constant. (U1-2)ext=ΔT

*…show more content…*For example anywhere on the body, there are two parallel forces F acting in the plane of motion of a body. The forces are acting oppositely directions, and R is the perpendicular distance between these forces which are called force couple and they exert a moment on that body.

The moment of a force is anywhere this force couple is located relative to an arbitrary point O, they will always exert the same moment. The direction of the moment due to this couple is given by the right hand rule and it is perpendicular to the plane containing the force pair. The magnitude of the moment Mo caused by the force couple is given by:

If the body rotates in the plane between two angles α1 and α2, the work done by Mo on the body is given by

where α is measured in radians.

If Mo is constant