Quiz 12, Problem 4
(2 points possible)
A uniform rod of length d is initially at rest on a flat, frictionless table. The rod is pivoted about a point a distance d/3 from one of its ends, and is free to rotate on the table about this pivot. A small glob of clay (mass m) starting at a distance r1 away from the pivot point moving with speed v, hits the rod after traveling a distance of r2 and sticks to it at the point of impact at a distance d/3 from the pivot, as shown at right. The rotational inertia of a rod about its center of mass is 112Md2
Note: The diagram at right shows a top view. Gravity points into the page.
Relative to the pivot, what is the initial angular momentum of the small disc before the collision? Use the sign convention indicated in the diagram.
Symbol m v d r1 r2 θ
You could enter m v d r_1 r_2 theta
Li=
unanswered
If the mass of the rod has mass 4m what is the magnitude of the angular velocity of the rod+clay system after the collision?
ω=
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sweg
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What is thou answer
To find the initial angular momentum of the small disc, we need to use the formula:
Li = m * v * r1 * sin(theta)
where
m is the mass of the small disc,
v is the speed of the small disc,
r1 is the distance of the small disc from the pivot point,
and theta is the angle between the direction of motion of the small disc and the line connecting the pivot and the small disc.
Plugging in the given values:
m = ?
v = ?
r1 = ?
theta = ?
You need to provide the values of m, v, r1, and theta in order to calculate the initial angular momentum (Li).
To find the magnitude of the angular velocity of the rod+clay system after the collision, we need to use the principle of conservation of angular momentum.
Angular momentum before the collision (Li) = Angular momentum after the collision (Lf)
The initial angular momentum (Li) can be calculated using the formula given above.
The final angular momentum (Lf) of the system is the sum of the angular momentum of the rod and the clay stuck to it.
Lf = I * omega
where
I is the moment of inertia of the system,
omega is the angular velocity of the system.
Given that the moment of inertia of the rod about its center of mass is 112Md^2, and the mass of the rod is 4m, we can calculate the moment of inertia of the system (I) as:
I = (112Md^2) + (4m * (d/3)^2)
Then, by substituting the calculated values of I and solving the equation Lf = I * omega, we can find the magnitude of the angular velocity (omega) of the rod+clay system after the collision.
Plugging in the given values:
M = ?
d = ?
You need to provide the values of M and d in order to calculate the magnitude of the angular velocity (omega).