Question

Could you please help with question 18-20

+ d - 7 17. [1pt] A wheel of mass m = 1.87 kg and moment of inertia, 1= 1.530 kg.m' is supported by a pivot a distance d=0.17 m from the wheel, as shown in the diagram. The axle through the wheel is initially in the horizontal plane, as shown, and the wheel is spinning about the axis in the sense indicated, with an angular velocity o = 90 rad/s. Answer the following three questions using the choices given; e.g., if the answer to the first question is A, and to the second and third question, B, enter ABB. You only have 7 tries! i) Assuming that the majority of the angular momentum of the wheel comes from the spinning of the wheel about its axis, what is the direction of the angular momentum vector? A)-î B) C) î D)k E)ſ F)-ſ G) None of these ii) The force of gravity acts on the wheel. What is the direction of the torque (vector) that acts on the wheel about the pivot point? A) -î B) C) D) - E)F)-î G) None of these iii) Recall that T = dL/dt, hence AL = TAt, and new = Lold+AL. In response to the conditions above, in addition to spinning about the axle, the axle and wheel will A) precess (i.e., rotate in the horizontal plane) about the z-axis in a clockwise sense when viewed from above. B) precess about the z-axis in a counter-clockwise sense when viewed from above. C) rotate downward in the vertical plane that contains the axle and the support. Yes, Computer gets: CEB 18. [1pt] Calculate the magnitude of the angular momentum of the wheel in the initial position shown in the diagram. Angular momentum units are kg*m^2/s Answer: Submit All Answers) 19. [1pt] Calculate the magnitude of the torque on the wheel about the pivot in the initial position shown in the diagram. Answer: Submit All Answers 20. [1pt] Calculate the magnitude of the angular velocity with which the wheel and axle precess about the pivot point. Answer: Submit All Answers )

Answer 1

18. Initial angular momentum = I $\omega$ = 1.530 $\times$ 90 $\approx$ 138 kg m² s^-1

19. Torque = mg $\times$ d = 1.87 $\times$ 9.8 $\times$ 0.17 = 3.115 N m

20. magnitude of angular velocity $\omega$ _p with which the wheel and axle precess

$\omega$_p = mgd / ( I $\omega$ ) = ( 1.87 $\times$ 9.8 $\times$ 0.17 ) / 138 = 0.0226 rad/s