Asolid disk of mass m1 . 9.7 kg and radius R-0.25 mis rotating with a constant a

Question

Asolid disk of mass m1 . 9.7 kg and radius R-0.25 mis rotating with a constant angular velocity of -39nd/s. Athin rectangular rod with mass m2-3.8 kg and length L-2R-0.5 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk 1) What is the initial angular momentum of the rod and disk system? mIs Submit You currently have 1 submissions for this question. Only 10 submission are allowed You can make 9 more submissions for this question 2) What is the initial rotational energy of the rod and disk system? J Submit You currently hove O submissions for this question. Only 10 submission are allowed. You con make 10 more submissions for this question 3) What is the final angular velocity of the disk? 30.9 You currently have 1 submissions for thls question. Only 10 submission are allowed. You can make 9 more submissions for this question. /s Submit 4) What is the final angular momentum of the rod and disk system? You currently have 2 submissions for this question. Only 10 submlssion are ollowed. You can moke 8 more submissions for this question 5) What is the final rotational energy of the rod and disk system currently hove O submissions for this question. Only 10 subméssion are alloned. You can make 10 more submissions for this question )The rod tookt-5.1 s to accelerate to its final angdar speed with the disk What average torque was rod by the disk? You currently have 1 submissions for this question Only 10 submission are allowed. You con make 9 more submissions for this question.

Explanation / Answer

1) initial angular momentum = Idisk*w = 0.5MR2*w = 0.5*9.7*0.252*39 = 11.821 kg-m2/s

2) Initial rotational energy = 0.5*Idisk*w2=0.5*0.5*9.7*0.252*392= 230.52 J

4) Final Angular momentum = (Idisk+Irod)*w' {where w' is the new angular velocity}

Idisk=MR2=0.3031

Irod = mL2/12 =0.0794; w'=30.9 rad/sec

Final Angular momentum = (0.3031+0.07914)*30.9 = 11.819 which is approximately equal to the initial angular momentum, the asnwer to this part can also be found out by conservation of angular momentum.

5) Final energy = 0.5*(Idisk+Irod)*w'2 =0.5*(0.3031+0.07914)*30.92= 182.60 J

6) using equation of rotation motion,

w'=w+*t

=-1.588 rad/s2 {negative sign indicates deceleration}

Torque=Irod = 0.07194*1.588 = 0.1142 N-m

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