Need verify on a momment of inertia/torque problem

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In summary, a student is seeking help with a physics problem involving the moment of inertia and torque applied to a solid disc. After providing the necessary calculations, the student admits to struggling with these types of problems and seeks corrections and advice. The expert suggests paying attention to units in calculations and reminds the student to post future problems in the correct section.
  • #1
Hi, this is my first time on this forum, so don't flame me for not doing things right. I'm a junior in high school and currently taking AP physics, this problem in my hwk has been bothering me for a while. I've never received the answer to this question and i just need to know if i did this right, since this is really the first moment of inertia problem i encountered...
the problem is:
A force of 15N is applied tangentially to the edge of a 0.88kg solid disc initially at rest. The radius of the disc is 0.55m. How fast will the disc be spinning after it has gone 3.0 complete rotations? (disregard all the friction/air resistance etc.)

The moment of Inertia of a solid disc is I=1/2mr^2 >> I=1/2(0.88)(0.55^2) >> I=0.1331
Torque= Lever arm x Force applied Torque= 15N x 0.55m = 8.25Nm
Torque = alpha x I >>> 8.25= alpha x 0.1331 >>> alpha = 62 (this doesn't look right :cry: )
Then just use Kenematic Equations
since 3 rotations is 6pi
W^2=0(62)(6pi)>>> W= 48.35radians/sec (this doesn't look right either :mad: :cry: )

Basicly my thoughts through the problem ^^^^^^^^^
Feel free to correct me on watever...i admitt, i suck/hate these problems.
Thanks :biggrin:
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  • #2
I have not verified your numbers, but the approach is correct.

I will suggest that you make it a habit to carry the units along in your calculations. Properly used, units can be a real aid in arriving at the correct solution.

Note: I have moved this post to the homework help section. In the future please post such problems here... Welcome to Physics fourms.
  • #3

Hello, and welcome to the forum! It's great to see you taking an interest in physics and seeking help when you need it.

First of all, your moment of inertia calculation is correct. Good job on that! However, there are a few things that need to be corrected in your solution.

Firstly, the torque equation should be written as T = I * alpha, not T = alpha * I. This means that the alpha value you calculated is actually 0.1331 * 8.25 = 1.10 rad/s^2. This is a more reasonable value for acceleration.

Next, when using the kinematic equations, it's important to use consistent units. You have used radians for your angular velocity (W) and time (Theta), but have used Nm for your torque. To be consistent, you should use units of kgm^2/s^2 for your torque. This gives you a value of 8.25 kgm^2/s^2 for your torque.

Plugging this into the equation W^2 = Wo^2 + 2(alpha)(Theta), you get W = 7.06 rad/s. This is a more reasonable answer for the angular velocity after 3 rotations.

I hope this helps and clears up any confusion. Keep up the good work!

1. What is a moment of inertia?

A moment of inertia is a measure of an object's resistance to changes in rotation. It is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation.

2. Why is it important to verify the moment of inertia in a torque problem?

Verifying the moment of inertia in a torque problem ensures that the correct amount of force is applied to produce the desired rotational acceleration. Using the wrong moment of inertia value can lead to inaccurate calculations and incorrect results.

3. How do you calculate the moment of inertia?

The moment of inertia can be calculated using the formula I = Σmr², where I is the moment of inertia, Σm is the sum of the masses of all the particles in the object, and r is the distance from each particle to the axis of rotation. Alternatively, there are specific formulas for calculating the moment of inertia for different shapes, such as cylinders, spheres, and disks.

4. Can the moment of inertia be negative?

No, the moment of inertia cannot be negative. It is a physical property of an object and represents its resistance to changes in rotation. A negative moment of inertia would indicate that the object has a negative amount of resistance, which is not possible.

5. What are some common units for moment of inertia?

The SI unit for moment of inertia is kilogram-meter squared (kg·m²). Other common units include gram-centimeter squared (g·cm²) and pound-foot squared (lb·ft²).

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