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Consider a right-angle triangle lying in the xy plane with its corners at ( x , y , z ) = (1,0,0), (0,1,0), and the origin. A blue dot is now painted...
Consider a right-angle triangle lying in the xy plane with its corners at ( x , y , z ) = (1,0,0), (0,1,0), and the origin. A blue dot is now painted on the corner of the triangle at the origin. At time t = 0, the blue dot is kicked : an impulse k z-hat is delivered to this corner, where k is a positive constant with units of momentum. Ignore gravity.
(a) Calculate the velocity vector of the blue dot at time t = 0+, immediately after the impulse is delivered.
(b) Calculate the velocity vector v ( t ) of the blue dot at all times t > 0.
Hint 1: After the impulse is applied, there are no external forces and no external torques on the triangle.
What, therefore, are the conserved quantities for its subsequent motion?
Hint 2: Note carefully the direction of ! ω t = 0 + from part (a). Is it along a principal axis (PA)?
The time-dependence of ω ( t ) will be greatly simplified if ! ω starts out parallel to a PA.
