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To see this, let’s take a simple example of two masses at the end of a massless (negligibly small mass) rod (Figure \(\PageIndex{1}\)) and calculate the moment of inertia about two different axes. In this case, the summation over the masses is simple because the two masses at the end of the barbell can be approximated as point masses, and the ...
- 10.3: Dynamics of Rotational Motion - Rotational Inertia
Understand the relationship between force, mass and...
- 10.3: Dynamics of Rotational Motion - Rotational Inertia
Example 1. Simple translational mass-spring-damper system. A body with mass m is connected through a spring (with stiffness k) and a damper (with damping coefficient c) to a fixed wall. An external force F is pulling the body to the right. We want to extract the differential equation describing the dynamics of the system.
Purdue University – ME365 – Rotational Mechanical Systems General Mechanical Systems • Example Derive the differential equation of motions (EOMs) for the system in terms of the outputs x and θ, and the input u(t). FBD:
Rotational Motions of Mass: The inertia property is a function of the mass distribution as described by its mass moment of inertia about its center of mass or a fixed point O. When the mass oscillates about a fixed point O or a pivot point O, the rotary inertia J o J o is given by the parallel-axes theorem: J o = J G +md2 J o = J G + m d 2.
Understand the relationship between force, mass and acceleration. Study the turning effect of force. Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration.
By the end of this section, you will be able to: Understand the relationship between force, mass and acceleration. Study the turning effect of force. Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration.
mass of a three-dimensional rotating body on its motion, defining the principal axes of a body, the inertia tensor, and how to change from one reference coordinate system to another. We now undertake the description of angular momentum, moments and motion of a general three-dimensional rotating body.
