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Rotational Motion. We are going to consider the motion of a rigid body about a fixed axis of rotation. The angle of rotation is measured in radians: . (rads) . s. (dimensionless) r. s . Notice that for a given angle , the ratio s/r is independent of the size of the circle. . r. Example: How many radians in 180o?
Mass moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration ( Ù) about an axis of rotation (a larger mass moment of inertia around
13.1.1 Examples of rigid bodies. Our first example of a rigid body is of a wheel rolling with constant angular velocity ̇φ = ω, and without slipping, This is shown in Fig. 13.1. The no-slip condition is dx = R dφ, so ̇x. CM = V = Rω. The velocity of a point within the wheel is. v = VCM + ω × r , (13.3) 1.
Purdue University – ME365 – Rotational Mechanical Systems • EOM of a simple Mass-Spring-Damper System We want to look at the energy distribution of the system. How should we start ? • Multiply the above equation by angular velocity term : What have we done ? • Integrate the second equation w.r.t. time: What are we doing now ?
Rotational Motion: Moment of Inertia. 8.1 Objectives. Familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body as mass plays in the description of linear motion. Investigate how changing the moment of inertia of a body a ects its. •. rotational motion.
The moment of inertia of a body rotating around an arbitrary axis is equal to the moment of inertia of a body rotating around a parallel axis through the center of mass. plus the mass times the perpendicular distance between the axes h squared. Solid sphere of radius R rotating around symmetry axis: I = 2MR2/5. I = ICOM+Mh2. If R<<h. ICOM <<< Mh2.
6.4.4 Example: The system rotates about the k axis with angular speed . Find formulas for its angular momentum and kinetic energy: (a) Using the formula in terms of the inertia matrix (b) By summing the contributions from the individual particles directly z) ho : z k 9 h Z (m Lx-tm + mg page 8
