一个奇怪的lab经历

    这几天AP物理学到rotation，老师就出了一个lab：假设这是僵尸末日时代，你有两种武器，一种是一个质量全部集中在中间的棒子，另一个质量分别在两边，中空。请证明哪个武器更好。

    怎么说呢，证明的方法五花八门。我原先的做法是比较转动能量。我先用积分积出物体的转动惯量，再用自己瞎推出来的”不严谨公式”，最后得出的结果在相同torque相同转轴等条件下，边空的棒子有更大的转动惯量。后来和学霸学姐一交流，一下发现rotational energy在这种情况应该相等才对。然后心态就有点崩。。。刚刚用了一个评判标准和方法，做出了一个新的lab report（然而水平还是渣渣）。哎。。。心塞。

    在此贴文给作为一个物理学渣的自己留下一点小小的纪念。。。

    Zombie Apocalypse Lab

Scenario: In a post-apocalyptic world plagued by zombies, humans struggled to survive and developed two kinds of rods as weapons: one with mass concentrated on its center; the other with mass equally concentrated on its two ends. In this lab, we sought to find out, through estimation, which rod would make a more effective weapon. We ignored the rods’ own body masses and focused on their inner masses.

Estimation: We assumed that to hit any zombie, the hitter would stand still, give the rod at hand a force at its one end and rotate it around its center of mass axis (a normal hitting pose). We decided to radically simplify our calculation by setting the concentrated masses as simple particles. Therefore, I1st = 2*0.71*0.45^2 = 0.29kg*m^2. For the second rod, we set two mass particles to locate at 5cm to the center of mass (rotational axis) and are on opposite sides. Therefore, I2nd = 2*0.71*0.05^2 = 0.00355kg*m^2.

To compare the rods’ lethality, we first decided to compare the time it takes for the two rods to have the same amount of angular momentum given that the hitter supplied the same, constant torque τ (as timing, we figure, is vital to survive in a post-apocalyptic zombie world). The change in angular momentum is the angular impulse ∑τ(t); when torque is constant, ΔL=τ*Δt. For angular momentums for both rods to equal each other, Δt is thus the same. Therefore, in this case, both rods are equally effective.

Now, however, given the same constant torque, to have the same angular displacement θ, Δt would be different. This is because as I1st>I2nd, α1=τ1/I1st < α2=τ2/I2nd, thus the time it takes for the 1st rod greater than that of the 2nd rod. In terms of rotating the rod to the same extent, 2nd proves to be a more effective weapon.