Is my solution correct? About Rotational motion

[noppawit]

A rigid body is made of three identical thin rods, each with length L=0.60m, fastened together together in the form of a letter H. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of H. The body is allowed to fall from rest from a position in which the plane of the H is horizontal. What is the angular speed of the body when the plane of the H is vertical?

I am quite not sure that can I change g (gravity) to α (Angular acceleration) by using gr = α

For my solution,
α (Angular acceleration) = g/r = 9.81/0.6 = 16.4 rad/s²

θ = 90 radian, as it said fall from plane of the H is horizontal to H is vertical.

ω² = ω₀²+2aθ
ω² = 0 + 2(16.4)(90)

Answer is 54.3 rad/s


Am I all correct? I'm quite not sure especially angular acceleration.

Thank you

 

[Doc Al]

I am quite not sure that can I change g (gravity) to α (Angular acceleration) by using gr = α

For my solution,
α (Angular acceleration) = g/r = 9.81/0.6 = 16.4 rad/s²

That's not how you'd find the angular acceleration. If you wanted the angular acceleration (not needed for this problem, by the way), you'd find the torque acting on the body and the body's rotational inertia about the axis. Note that the angular acceleration changes as the object falls, so kinematic equations that assume constant acceleration will not apply.

Instead of all that, consider the energy changes as the body falls. Hint: Since the body rotates about a fixed axis, you can consider its kinetic energy as purely rotational.

 

[noppawit]

I still can't solve this problem. Can anybody give me a starter equation?

Thank you.

 

[tiny-tim]

Hi noppawit!

What is the angular speed of the body when the plane of the H is vertical?

Hint: What is the KE of the body when the plane is vertical?

 

[Doc Al]

To add to what tiny-tim said, what's the general formula for the rotational KE of a rotating body?

 

[noppawit]

1/2iω²

 

[Doc Al]

1/2iω²

Good. Rotational KE = 1/2 I \omega^2. What other kind of energy is relevant to this problem? What's the rotational inertia (I) of the body about its axis?