Question

Three small balls of mass 3.7 kg, 2.4 kg, and 3 kg are connected by light rods laying along the y-axis. The rod connecting the first and second balls is 4.8 m long and the rod connecting the second and third balls is 1.9 m. The entire system rotates around the x-axis, which is between the first and second balls and a distance 2.6 m from the first ball, at a rotational speed 2.4 s^-1

(a) What are the linear speeds of the three objects?
First Object:
Second Object:
Third Object:   

(b) What is the linear kinetic energy of each of the balls?
First Object:  
Second Object:  
Third Object:  

(c) What is the total kinetic energy of the system?


(d) What is the moment of inertia around the x-axis of each of the balls?
First Object:
Second Object:
Third Object:

(e) What is then rotational kinetic energy of each of the balls?
First Object:
Second Object:
Third Object:

(f) What is the rotational kinetic energy of the system?


(g) What is the distance of the center of mass of the system from the first ball?


(h) What moment of inertia of each ball around the center of mass?
First Object:
Second Object:
Third Object:

(i) What is the moment of inertia of the system with respect to the center of mass


(j) What is the moment of inertia due to the shift of the rotational axis from the center of mass to the x-axis?


(k) What is the moment of inertia of the system around the x-axis?


(l) What is the linear speed of the system?


(m) What is the rotational speed of the system?


(n) What is the linear kinetic energy of the system?


(o) What is the rotational kinetic energy of the system?


(p) What is the total kinetic energy of the system?

Answer 1

I have answered first 4 question only as we are instructed to attend oonly first part of a question unless specified.

>x-asis - ON wa angular relocity Lets suppose the masses are mi = 3.9 kg, m2 = 24 kq, m3 = 3 kg, comected on the rod at a distance from X-axis, 8, 82 and 8 respectively, u As has been mentioned, the distance between first ball (mi) and second ball (m2) is, 8+82 = 4.8m. - (1) and the same for second ball (one) and third ball (mg) 18, B 82 = 1.am. (2). Hence, The distance of first ball from x-axis, &i=2.60m. Therefore using (1) and (2), we desire, 12=2.2m, and, 8 = 41m. The, angular velocity of each par object is, W = 2.4 81. Hence, linear speed of, (1) First object 29 = wr = 216 x 2.4 m/8= 6.24 m/s (2) Second Object, Vo = wr2 = 24 x 2.2 m/s = 5.28 m . (3) Third Object, Vo = wrz = 2.4 x 4 ) m = 9.84 m/s.

(6) The linear Kinetic energy of each object, St (1) First object : miv * 3.7 X 6.242 = 72.03456 J (2) Second object mv = 1* 2.485.28%= 33.45408 J (3) Third object, I may = + x 3x9.84² = 145.2384. I (c) The total kinetic energy of the system is in Loint-mart song va = 250.72704.J . (d) The moment of Inertia of each of the balls are, 1 First Object, I = mis² = 3.7x2.6² = 25.012 kg. m² 29 Second Objedd, I2 = meo2 = 24% 2,22 = 1.616 kg.om? (3) Third object, Ig-mzoz = 3 x 4.12 - 50.43 kg, m?