A parade leader tosses his baton straight up into the air from one end, causing

Question

A parade leader tosses his baton straight up into the air from one end, causing the baton to rotate with ? = 6 rad/s, as well as travel vertically upward with a center-of-mass speed of 4 m/s. The baton consists of a thin, mass-less rod with 0.8 kg masses on each end. (Hint: Model the moment of inertia of the baton as simply two point particles each with M = 0.8 kg at the same distance from their axis of rotation.)

a) Find the magnitude of the angular momentum of the baton about an axis through the center of mass, perpendicular to the plane of rotation of the baton.

b) Find the total kinetic energy of the baton.

Explanation / Answer

a) moment of inertia of baton about its center, I = 2*M*r^2

= 2*0.8*(1/2)^2

= 0.4 kg.m^2

angular momentum, L = I*w

= 0.4*6

= 2.4 kg.m^2/s

b) Total kinetic energy = translational KE + rotational KE

= 0.5*(2*M)*Vcm^2 + 0.5*I*w^2

= 0.5*(2*0.8)*4^2 + 0.5*0.5*6^2

= 20 J

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