- #1

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Hello! :)

When solving a problem, I had to calculate the angular velocity of a homogenius rod when it comes to vertical position, after being released from a horisontal position (the rod is fixed at one end). This is as usually done with energy conservation, using the rotational energy of the rod and setting it equal to the change in gravitational potential energy. If the lenght of the rod is L and its mass m, the following is obtained (Δh=L/2):

mL

--> ω = (3g/L)^(1/2)

However, I started wondering if this problem could be solved using translational kinetic energy instead. If we consider the center of mass (CM):

mv

--> v = (Lg)^(1/2)

--> ω = v/(L/2) = 2 (g/L)^(1/2)

As seen, this does not yield the same answer as if we use rotational kinetic energy.

My question is: Why can't translational kinetic energy be used to calculate the angular velocity? or if it can be used: Where am I thinking wrong?

Thank you very much!

When solving a problem, I had to calculate the angular velocity of a homogenius rod when it comes to vertical position, after being released from a horisontal position (the rod is fixed at one end). This is as usually done with energy conservation, using the rotational energy of the rod and setting it equal to the change in gravitational potential energy. If the lenght of the rod is L and its mass m, the following is obtained (Δh=L/2):

mL

^{2}/3 *ω^{2}/2 = mgL/2--> ω = (3g/L)^(1/2)

However, I started wondering if this problem could be solved using translational kinetic energy instead. If we consider the center of mass (CM):

mv

^{2}/2 = mgL/2--> v = (Lg)^(1/2)

--> ω = v/(L/2) = 2 (g/L)^(1/2)

As seen, this does not yield the same answer as if we use rotational kinetic energy.

My question is: Why can't translational kinetic energy be used to calculate the angular velocity? or if it can be used: Where am I thinking wrong?

Thank you very much!