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Equilibrium,Torque and Angular Momentum

Equilibrium,Torque and Angular Momentum. Lecture 10 Tuesday: 17 February 2004. Defining Rotational Inertia. The larger the mass, the smaller the acceleration produced by a given force.

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Equilibrium,Torque and Angular Momentum

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  1. Equilibrium,Torque and Angular Momentum Lecture 10 Tuesday: 17 February 2004

  2. Defining Rotational Inertia • The larger the mass, the smaller the acceleration produced by a given force. • The rotational inertia I plays the equivalent role in rotational motion as mass m in translational motion. • I is a measure of how hard it is to get an object rotating. The larger I, the smaller the angular acceleration produced by a given force.

  3. Determining the Rotational Inertia of an Object I is a function of both the massand shape of the object. It also depends on the axis of rotation. • For common shapes, rotational inertias are listed in tables. A simple version of which is in chapter 11 of your text book. • For collections of point masses, we can use : • where r is the distance from the axis (or point) of rotation. • For more complicated objects made up of objects from #1 or #2 above, we can use the fact that rotational inertia is a scalar and so just adds as mass would.

  4. Torque as a Cross Product (Like F=Ma) The direction of the Torque is always in the direction of the angular acceleration. • For objects in equilibrium, =0 AND F=0

  5. Torque Corresponds to Force • Just as Force produces translationalacceleration (causes linear motion in an object starting at rest, for example) • Torque produces rotational acceleration (cause a rotational motion in an object starting from rest, for example) • The “cross” or “vector” product is another way to multiply vectors. Cross product results in a vector (e.g. Torque). Dot product (goes with cos ) results in a scalar (e.g. Work) • r is the vector that starts at the point (or axis) of rotation and ends on the point at which the force is applied.

  6. Does an object have to be moving in a circle to have angular momentum? • No. • Once we define a point (or axis) of rotation (that is, a center), any object with a linear momentum that does not move directly through that point has an angular momentum defined relative to the chosen center as

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