Determine the angular momentum of the following: Idisk = 1/2 MR^2 All values sho

Question

Determine the angular momentum of the following: Idisk = 1/2 MR^2 All values should be in base units: kg, m, sec etc. i) A disk, mass 50 kg and radius 60 cm which turns one revolution in 15 msec (milliseconds). ii) A baseball, thrown 60 cm over home plate (the center). Baseball has mass of 145 grams and speed of 40 m/sec (meters per second) b) A disk of mass 50 kg and radius 80 cm is initially spinning at 14 rad/sec. A sticky ball of mass 20 kg is onto it at a position of 60 cm from its center. What will be the final angular speed of the system? a) A cylinder containing glycerin, density 1260 kg/m^3, has a radius of 25 cm and a height of 75 cm. What is the Weight of glycerin in this cylinder? b)A fireman at ground level (y = 0) wishes to put out a fire in a building 30 m high. She starts with water coming into the hose with back pressure 201.300 kPa (kilopascals) and velocity 20 m/sec. At the top of building, the pressure is Atmospheric (101.3 kPa).What velocity will this water (density of 1000 kg/m^3 have coming out of the hose at the top of the building? (Make sure all units used are in base value !)

Explanation / Answer

ii) M= mv = (145 x 10^-3) ( 40) = 5.8 kg m/s

b) conserving the angularmomnetum

I1w1= I2 w2

( 50 ) (80 )^2 ( 10^-4) ( 14) = [ ( 50 ) (80 )^2 ( 10^-4) + 20 x ( 60 )^2 x 10^-4 ) w

4480000 = 392000 w

w= 11.428 rad/sec

a) weight = mass x g = ( voulme x density ) 9.8= 1363.103 N apprx

b) Using Bernoulli's theorem,

201.300 x 10^3 + 1/2 (1000) ( 20)^2 = 101.3 x 10^3 + 1/2 ( 1000) v^2 + (1000) (9.8) (30)

201300 + 200000- 101300 - 294000= 500 v^2

v= 3.464 m/s a pprx

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