What is plane motion of rigid bodies?
A rigid body is said to perform plane motion when all parts of the body move in parallel planes. If every line in the body remains parallel to its original position at all times, the body is said to be in translation motion. All the particles forming a rigid body move along parallel paths in translation motion.
What is the formula of rigid body?
For a rigid body, the angular momentum (L) is the product of the moment of inertia and the angular velocity: L = Iω. For a point of mass, angular momentum can be expressed as the product of linear momentum and the radius ( r): L = mvr.
What is rigid body with example?
A rigid body is an idealization of a solid body in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it. Example: A metal rod in an example of rigid body.
What is the plane motion?
Motion in a Plane. Motion in a plane is also referred to as a motion in two dimensions. For example, circular motion, projectile motion, etc. For the analysis of such type of motion, the reference point will be made of an origin and the two coordinate axes X and Y.
What are the different types of plane motion of rigid bodies give suitable example?
The two types of motion a rigid body can undergo are;
- Translational Motion.
- Rotational Motion.
What are the conditions of equilibrium of a plane rigid body?
Here are the two conditions for equilibrium and their respective equations. (1) The total or net force i.e. the vector sum of all the forces, on the rigid body is zero. (2) The total Torque i.e. the vector sum of the torques on the rigid body is zero.
How do you find the equilibrium of a rigid body?
For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point O must be equal to zero.
What are some examples of rigid bodies in physics?
– Examples: Smoke, Fire, Water, Wind, Leaves, Cloth, Magnets, Flocks, Fish, Insects, Crowds, etc.
What 3 conditions must be met to have equilibrium in a 2 dimensional plane?
Conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of equilibrium). These two conditions must be simultaneously satisfied in equilibrium.
What is the equation of equilibrium?
Solution: In order for a system to be in equilibrium, it must satisfy all three equations of equilibrium, Sum Fx = 0, Sum Fy = 0 and Sum M = 0.
What is kinematic constraint?
Kinematic constraints are equations that control the motion of solids, faces, edges, or points. Add a Prescribed Displacement constraint to enter expressions for constraints. You can define the equations using predefined coordinate systems as well as custom coordinate systems.
What are the properties of a rigid body?
A rigid body is an idealization of a body that does not deform or change shape. Formally it is defined as a collection of particles with the property that the distance between particles remains unchanged during the course of motions of the body.
How do rotations feature in the kinematics of rigid bodies?
Here, we discuss how rotations feature in the kinematics of rigid bodies. Specifically, we present various representations of a rigid-body motion, establish expressions for the relative velocity and acceleration of two points on a body, and compare several axes and angles of rotation associated with the motion of a rigid body.
What are the characteristics of rigid bodies?
Chapter 15 KINEMATICS OF RIGID BODIES Chapter 15 KINEMATICS OF RIGID BODIES In rigid body translation, all points of the body have the same velocity and the same acceleration at any given instant.
How do we determine the motion of a rigid body?
It is well known that knowledge of the position vectors of three material points suffices to determine the motion of a rigid body. Indeed, this is the premise for optical tracking schemes and is the motivation for our construction of a corotational basis. Referring to Figure 4, we start by picking three material points of a body: , , and .
What is the acceleration of a rigid body with a fixed point?
In three dimensions, the most general displacement of a rigid body with a fixed point Ois equivalent to a rotation of the body about an axis through O. The angular velocity wand the instantaneous axis of rotation of the body at a given v= = wxr dr dt Differentiating this expression, the acceleration is instant can be defined.