College Physics 8.1

College Physics 8.1 - 8.1 College Physics Kinetic energy...

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8.1 College Physics Kinetic energy has rotational and translational Translational is ½ mv^2. To express this in rotational form, use angular velocity. Equation is v=rw where w is angular velocity. So KE translational = ½ mr^2w^2 = KE rotational To find the KE rotational, we need to find the KE rotational of every point. So we need to find the sum. Only angular velocity w, changes. The rest are constants. Mass and r are constants. Thus we can express the sum of mass times radius with a new variable, I. KE rotational = ½ Iw^2 I is called rotational inertia or how hard it is to change its angular velocity. It is also called moment of inertia. For rotational inertia, since it is a sum, divide and conquer can be used for objects. Since only mass and radius are taken into account for rotation, objects can be compressed as long as mass stays the same. Thus door problems around a hinge can be thought of as a rod around the same axis with the same mass. Rotational kinetic energy is included in the mechanical energy. W nc= Delta K + Delta U = Delta E mech K = K tr + K rot Note nc = non-conservative
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8.2 Torque Torque is related to force. Torque is to rotation as force is to translation. Torque is a measure of how effective a given force is at twisting or turning something Torque can change rotational motion by slowing it down or speeding it up It is impossible to do torque without doing force. Thus when two hands are trying to stop the bike wheel, the net force might be zero but the torque is not because both are slowing it down. The magnitude is the same but the direction is the same as well. Torque depends on direction and distance. If push a heavy door perpendicular to the axis of rotation, torque is high If push it radially towards axis, torque is zero. If at an angle, only perpendicular counts The higher the distance the stronger the torque Thus torque = tau = +- rF where F is force perpendicular and r is shortest distance between rotation axis and point of application Torque unit is Nm which is the same as the SI unit for energy. However joule is not the same as torque and torque is not an energy. These are not interchangeable. Sign of torque indicates direction of angular acceleration that torque would cause by itself. Positive angular velocity means counterclockwise, CCW and negative is CW
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This note was uploaded on 04/05/2009 for the course ASTRO 101 taught by Professor Lloyd during the Spring '08 term at Cornell.

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College Physics 8.1 - 8.1 College Physics Kinetic energy...

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