Is my solution correct? About Rotational motion

In summary, the problem involves a rigid body made of three thin rods fastened together in the shape of an H, free to rotate about a horizontal axis. The body is released from rest in a horizontal position and falls to a vertical position. To find its angular speed in the vertical position, we can consider the change in kinetic energy as the body falls, using the formula for rotational kinetic energy (1/2 I \omega^2) and the body's rotational inertia about its axis.
  • #1
noppawit
27
0
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
 
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  • #2
noppawit said:
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
:confused: 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.
 
  • #3
I still can't solve this problem. Can anybody give me a starter equation?

Thank you.
 
  • #4
Hi noppawit! :smile:
noppawit said:
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? :smile:
 
  • #5
To add to what tiny-tim said, what's the general formula for the rotational KE of a rotating body?
 
  • #6
1/2iω2
 
  • #7
noppawit said:
1/2iω2
Good. Rotational KE = [itex]1/2 I \omega^2[/itex]. What other kind of energy is relevant to this problem? What's the rotational inertia (I) of the body about its axis?
 

FAQ: Is my solution correct? About Rotational motion

How do I know if my solution for rotational motion is correct?

The best way to determine if your solution for rotational motion is correct is to check it against known equations and principles. Start by identifying the variables involved in the problem and make sure they are correctly represented in your solution. Then, plug in the numbers and see if your solution matches the expected result. If it does, then your solution is likely correct.

What are some common mistakes to avoid when solving rotational motion problems?

Some common mistakes to avoid when solving rotational motion problems include not considering all the forces acting on an object, using the wrong equations or formulas, and not properly converting units. It is also important to check your answer for reasonableness and to make sure it has the correct units.

Is it necessary to use calculus when solving rotational motion problems?

It depends on the complexity of the problem. In some cases, calculus may be necessary to accurately solve for variables such as angular acceleration or torque. However, many rotational motion problems can be solved using basic algebra and trigonometry.

How can I improve my understanding of rotational motion?

To improve your understanding of rotational motion, it is helpful to practice solving a variety of problems and to familiarize yourself with the equations and principles involved. It may also be beneficial to work with a tutor or study with a group to discuss and compare solutions.

Can I use the same principles and equations for rotational motion as I do for linear motion?

While there are some similarities between rotational and linear motion, they are not interchangeable and use different equations and principles. It is important to understand the differences between the two in order to accurately solve problems involving rotational motion.

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