Question

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axis rod A wooden rod of length 40.0 cm and mass 1.00 kg is sitting on a frictionless horizontal surface. The rod has a pin through its centre so that it can freely rotate about a vertical axis perpendicular to the rod and passing through the center of the rod. A projectile of mass 0.0100 kg is now shot at the rod. The projectile is moving horizontally with a speed of 2.00 x 102 m/s in the direction perpendicular to the rod at the instant that it strikes one end of the rod. The projectile embeds in the rod. You may assume that the projectile embeds in the rod before the rod/projectile system starts to rotate. projectile (a) Just prior to the collision of the projectile with the rod, calculate the angular momentum of the projectile with respect to the vertical axis through the centre of the rod. (b) Calculate the moment of inertia of the rod/embedded projectile system with respect to the vertical axis through the centre of the rod. (c) Calculate the angular speed of the rod with embedded projectile.

Answer 1

Here we apply concept of angular momentum conservation and concept of superposition of moment of inertia and definition of angular momentum.

2 = 4oom n = 1 kg Mp = 0.óloots Voep = 2.00 x 102 /s = 200 M/S & Li = mp up h ap Angular of momentum of D i A projectile about vertical Haris passing through center 'C' before callision Li=8xď p=mop Y='1/2 counter clockwire From Right hand rule) o bi = 0.0100kg) (200m/s) (0.201) to Lj = 0.4 tag m2 faec: A Moment of Inertia of rod about & - Pcm = m L² 12 moment of inertia of projectile about & Ip = mp (2) =mp L2 Total moment of Inertia, It = p + I Let angulor speed finally = w How It = m +mptat + ont = 62 +0.040 ) thg 60.4m)?

IT= 0.01373 tog met - As Initial rod was at rest do for (Rod & Prorectile dystem, het external torque de zero therefore Cingular moment com of sye tena will be conserved (hi) are = (f) ays > 0-4 ty m2 to = 60-01373 ty m2) co >> co = 29:13 raad /sec)