8 Angular Momentum

8 Angular Momentum - Angular momentum So far all...

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Unformatted text preview: Angular momentum So far all translational quantities such as force, kinetic energy and power have their rotational analog . The analog of translational momentum is angular momentum. Angular momentum is denoted by the symbol L. Angular momentum is a vector quantity typically given the letter L . It is defined to be: Angular Momentum L = r x p = r x mv Angular Momentum Notice that in structure angular momentum looks a lot like torque: L = r x p = r x mv . The SI units of angular momentum are kgm 2 /s The right hand rule applies to angular momentum to yield its direction perpendicular to r and v. L = r x p = r x mv The value of L depends on the choice of origin O , since it involves the position vector of the particle relative to the origin. Notice above, as the coordinate origin is moved closer to m i , the angular momentum associated with m i decreases L = r x p = r x mv When a net force acts on a particle or system of particles, momentum changes so its angular momentum may change also because: L = r x p = r x mv . The question then is what does the rate of change of angular momentum equal with respect to time? ( 29 ) a m x r ( v m x v dt dv m x r v m x dt r d dt L d + = + = ( 29 v m x v = = dt L d = = F x r x r ) a m ( Thus: The above equation tells us that the rate of change of angular momentum, equals the torque, or the net force, applied to the object. Likewise, in translational movement, the rate of change of momentum equals the force applied to the object. = dt L d A turbine fan in a jet engine has a moment of inertia of 2.5kgm 2 about its axis of rotation. As the turbine is starting up, its angular velocity as a function of time is: = (40 rad/s 3 )t 2 a) Find the fans angular momentum as a function of time, and find its value at time t = 3.0 seconds b) Find the net torque acting on the fan as a function of time and the torque at t = 3.0 seconds a) Find the fans angular momentum as a function of time , and find its value at time t = 3.0 seconds A turbine fan I = 2.5kgm 2 about its axis of rotation. as a function of time is: = (40 rad/s 3 )t 2 L(t) = I = (2.5kgm 2 )[(40rad/s 3 )t 2 ] This is the angular momentum as a function of time. At three seconds the angular momentum would be: L(t) = I = (2.5kgm 2 )[(40rad/s 3 )3 2 ] = 900 kg m 2 /s b) Find the net torque acting on the fan as a function of time and the torque at t = 3.0 seconds L(t) = I = (2.5kgm 2 )[(40rad/s 3 )t 2 ] ( 29 ( 29 ( 29 t s rad m kg dt dt s rad m kg dt dL / 200 / 40 5 . 2 3 2 2 3 2 =...
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8 Angular Momentum - Angular momentum So far all...

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