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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 Lecture 10 Tuesday: 17 February 2004
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.
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.
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
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.
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