Question

1)A 1.0 kg mass is located at (2.3, 0, -7.9) m and moving at (0, 5.7, 3.9) m/s. What is the angular momentum of this mass about the origin?

	A.	(-3.0, 0.0, -76)
	B.	(13, -9.0, 45)
	C.	(45, -9.0, 44)
	D.	(45, -9.0, 13)
	E.	(-76, 0.0, -3.0)
	F.	(0.0, 0.0, 0.0)
	G.	(-13, 9.0, -45)
	H.	(-45, 9.0, -13)
	I.	(76, 0.0, 3.0)
	J.	(-45, 9.0, -44)
	K.	(-44, 9.0, -45)
	L.	(44, -9.0, 45)
	M.	(3.0, 0.0, 76)

2)A 4.8 kg mass moving in a circle (diameter = 4.9 m). The angular momentum varies in time as l = 9.6t². What is the net torque acting on the mass at 14.3 s?

3)A 38.4 kg child stands on a spinning platform that has been well maintained (neglect friction in the axle). Initially the platform is spinning at 4.2 rev/s while the child's arms are extended outward (holding some weights). The child then pulls the weights back to close to their body. What is the final angular speed of the platform? Assume that the child can be considered a cylinder with a diameter of 0.7 m, spinning along its center axis and the weights are point masses (2 kg each) that are initially 1.4 m away from the center of the child. Assume that the weights are at the outer edge of the "cylinder" (i.e., the child) in the final moment.

Answer 1

1)

m = mass = 1 kg

= 2.3 i + 0 j - 7.9 k

= 0 i + 5.7 j + 3.9 k

angular momentum is given as

= m (x )

= (1) ((2.3 i + 0 j - 7.9 k ) x (0 i + 5.7 j + 3.9 k))

= 45 i - 9 j + 13 k

D.	(45, -9.0, 13)

2.

L = angular momentum = 9.6 t²

Net torque is given as

= dL/dt

= d(9.6 t² )/dt

= 19.2 t

at t = 14.3

= 19.2 x 14.3 = 274.56