Determine the angular momentum L for the following systems a

Determine the angular momentum, L, for the following systems: a) A car of mass 1000 kg with a speed of 50 m/s on a circular track of radius 100 m relative to the center of the track. b) A 1. 6-kg pendulam bob at the end of a 2. 0 m string released from rest from a horizontal position. What is the angular momentum of the bob when it is at its lowest position relative to the center of circular path? c) A 1. 00 m long uniform rod of mass 2. 0 kg that rotates about its center of mass at a speed of 10 rad/sec d) A playgroung merry-go-round of radius 2. 00 m and mass 125 kg rotating at a speed of 5 rev/min. 10. A thin rod of mass M and length L is struck at one end by a ball of clay of mass m.

Solution

L= r x P= m(r x v)

a) L= 1000(100 x 50 x sin90)=5000000 kgm²/s

b) velocity at lowest position= v= (2gh)^0.5 = (2*9.81*2)^0.5= 6.264 m/s

L= 1.6(2x 6.264 x sin90)= 20.045 kgm²/s

c) The formula for angular momentum in terms of angular momentum is L=I

For the rod, I= ML²/12= 2x1x1/12 =1/6 kgm²

Also =angular velocity=10 rad/s(given)

L= 1/6 x 10= 1.667 kgm²/s

d) Merry go round can be considered as a circular disk with uniform thickness.

Following same procedure as in (c),

L= I

I= mr²/2 = 125x2x2/2 =250 kgm²

=5x2x3.14/60 rad/s= 0.523 rad/s

L= 250kgm²/s x (0.523 rad/s)= 130.83 kgm²/s