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Unformatted text preview: Chapter 11. Rotational Dynamics As we did for linear (or translational) motion, we studied kinematics (motion without regard to the cause) and then dynamics (motion with regard to the cause), we now proceed in a similar fashion We know that forces are responsible for linear motion We will now see that rotational motion is caused by torques Consider a wrench of length L=r F = rF r Torque Units of N m Not work or energy, do not use Joules is called the lever arm. Must always be perpendicular to the force If the force is not perpendicular to the level arm, we need to find the component that is perpendicular (either the force or the lever arm) r F F sin = rF sin If =0, then the torque is zero r Therefore, torques (force times length) are responsible for rotational motion Newtons 2 nd Law for Rotational Motion F=F t r m The torque for a point particle of mass m a distance r from the rotation axis is = rF t F t = ma t , a t = r = ma t r = mr 2 Axis of rotation Define I = mr 2 = Moment of Inertia for a point particle; a scalar, units of kg m 2 A rigid body is composed of many, many particles of mass m i which are r i from the axis of rotation Each of these masses creates a torque about the axis of rotation .... 2 2 2 2 2 1 1 1 r m r m = = m 1 m 2 r 1 r 2 Rotation axis Sum up all torques due to all particles = = = I r m I r m i i i i i 2 2 is the same for all particles I = moment of inertia for the rigid body. It is different for different shaped objects and for different axes of rotation. Table 10.1....
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