A turntable with a radius of 12cm is being explored by two bugs, one at 5cm from the center and another, very dizzy beetle at 2cm from the center. The turntable is spinning at 7 rad/s. Which bug will have the greater angular momentum?
To determine which bug will have the greater angular momentum, we need to calculate the angular momentum for each bug.
The angular momentum (L) of an object is given by the formula:
L = I * ω,
where I is the moment of inertia of the object and ω is the angular velocity.
The moment of inertia (I) of an object is given by the formula:
I = m * r^2,
where m is the mass of the object and r is the distance from the axis of rotation.
Given that both bugs are on the turntable, we can assume that their masses are the same.
Let's calculate the angular momentum for each bug:
For the bug at 5cm from the center:
r = 5cm = 0.05m
ω = 7 rad/s
Using the formula for moment of inertia, we can calculate:
I = m * r^2
Since the bug's mass is the same as the other bug on the turntable, we can ignore it for the comparison of angular momentum.
I = r^2 = (0.05m)^2 = 0.0025 kg·m²
Now, using the formula for angular momentum, we can calculate:
L1 = I * ω = 0.0025 kg·m² * 7 rad/s = 0.0175 kg·m²/s
For the bug at 2cm from the center:
r = 2cm = 0.02m
ω = 7 rad/s
Again, using the formula for moment of inertia, we can calculate:
I = r^2 = (0.02m)^2 = 0.0004 kg·m²
Now, using the formula for angular momentum, we can calculate:
L2 = I * ω = 0.0004 kg·m² * 7 rad/s = 0.0028 kg·m²/s
Comparing the angular momenta of the two bugs, we find that L1 (0.0175 kg·m²/s) is greater than L2 (0.0028 kg·m²/s).
Therefore, the bug at 5cm from the center will have the greater angular momentum.