Angular momentum is conserved, just before the clay hits and just after;
<span>mv(L/2) = Iw </span>
<span>I is the combined moment of inertia of the rod, (1/12)ML^2 , and the clay at the tip, m(L/2)^2 ; </span>
<span>I = [(1/12)ML^2 + m(L/2)^2] </span>
<span>Immediately after the collision the kinetic energy of rod + clay swings the rod up so the clay rises to a height "h" above its lowest point, giving it potential energy, mgh. From energy conservation in this phase of the problem; </span>
<span>(1/2)Iw^2 = mgh </span>
<span>Use the "w" found in the conservation of momentum above; and solve for "h" </span>
<span>h = mv^2L^2/8gI </span>
<span>Next, get the angle by noting it is related to "h" as; </span>
<span>h = (L/2) - (L/2)Cos() </span>
<span>So finally </span>
<span>Cos() = 1- 2h/L = 1 - mv^2L/4gI </span>
<span>m=mass of clay </span>
<span>M=mass of rod </span>
<span>L=length of rod </span>
<span>v=velocity of clay</span>
Answer: A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed.
Explanation:
3.4m/s
Explanation:
Given parameters:
Distance to school = 14.4km
Time taken by Amy = 49min
Time taken by bill = 20min after Amy = 20+49 = 69min
Unknown parameters:
How much faster is Amy's average speed = ?
Solution:
Average speed is the rate of change of total distance with total time taken.
Average speed = 
convert units to meters and seconds
1000m = 1km
60s = 1min
Distance to school = 14.4 x 1000 = 14400m
Time taken by Amy = 49 x 60 = 2940s
Time taken by Bill = 69 x 60 = 4140s
Average speed of Amy =
= 4.9m/s
Average speed of Bill =
= 1.4m/s
Differences in speed = 4.9 - 1.5 = 3.4m/s
Amy was 3.4m/s faster than Bill
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Answer:
(a)2.7 m/s
(b) 5.52 m/s
Explanation:
The total of the system would be conserved as no external force is acting on it.
Initial momentum = final momentum
⇒(4.30 g × 943 m/s) + (730 g × 0) = (4.30 g × 484 m/s) + (730 g × v)
⇒ 730 ×v = (4054.9 - 2081.2) =1973.7
⇒v=2.7 m/s
Thus, the resulting speed of the block is 2.7 m/s.
(b) since, the momentum is conserved, the speed of the bullet-block center of mass would be constant.

Thus, the speed of the bullet-block center of mass is 5.52 m/s.