The moment of inertia of a rigid body is the total number of moments of inertia of each particle that builds the object. Rigid objects are composed of many particles. 3.3 Moment of inertia of a homogeneous rigid body Has a smaller moment of inertia than the moment of inertia of the particle farther away from the axis of rotation. If we assume that the two particles above are rigid objects, then each particle that is near the axis of rotation.
Particles near the axis of rotation have smaller the moment of inertia, whereas particles that are far from the axis of rotation have greater the moment of inertia. Although the shape and size are the same because the location of the axis of rotation is different, the moment of inertia is also different. Determine the moment of inertia of the two particles, if:Ī) The axis of rotation is located between the two particlesī) The axis of rotation is at a distance of 0.5 meters from the particle with a mass of 2 kgĬ) The axis of rotation is at a distance of 0.5 meters from the particle with a mass of 4 kgīased on the results of the calculations above, the moment of inertia is strongly influenced by the location of the axis of rotation.
Two particles, each having a mass of 2 kg and 4 kg, are connected by a lightweight wire, where the wire length is 2 meters. What is the moment of inertia of particles when rotating? 3.2 Sample problems of the moment of inertia of the particleĪ particle with a mass of 2 kg was tied to a rope 0.5 meters long and then rotated. Equation 6 is used to determine the moment of inertia of a particle. I = moment of inertia of the particle, m = mass of the particle, r = distance between the particle with the axis of rotation. The moment of inertia of a particle is the product of the mass of the particle (m) and the square of the distance between particles with the axis of rotation (r 2 ). Equation 5 is the equation of Newton’s second law for rotating particles. Equation 5 states the relationship between the moment of force, the moment of inertia, and the angular acceleration of rotating particles. R F is the moment of force and m r 2 is the moment of inertia of the particle. Substitute a in equation 3 with a in equation 4: The relationship between tangential acceleration and angular acceleration is expressed by equation 4: The particles rotate so that the particles have angular acceleration. The relationship between force (F), mass (m), and the tangential acceleration of particles are expressed by equation 3:
After moved by the force of F, the particles move with a certain speed so that the particles have tangential acceleration. The particle is r apart from the axis of rotation. The particle with mass m is given the force F so that the particle rotates about the axis O.
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