Calculating Rotational Inertia and Yo-Yo Acceleration

In summary: The units should be cm/s^2.Part c. was plugging in the numbers. I was a little confused about r, r would be the radius of just the axel right? Using that, I got 20.4 cm/s^2.*** On edit ***Yes, it is the radius of the axle. However, your final answer should have units of cm/s^2.
  • #1
atm1993
3
0

Homework Statement


Given the following Rdisk = 2.50 cm, Raxle = 0.250 cm, Mdisk - 25.0g, Maxle = 0.750g

a. Determine the rotational inertia of a yo-yo about it's center.
b. Dervie using force and torque the expression for the linear acceleration of a yo-yo
c. Calculate the a of the yo-yo for the given values


Homework Equations



I = (1/2)mr^2
Iα = τ



The Attempt at a Solution



Part a. pretty simple, I think I did it right. Using the moment of inertia equation for a disk, just add 2xthe I of the disks, and the I of the axle, didn't have a problem for that, got 156gcm^2.

Part b. I wasn't completely sure if I was doing right. I started with mg-T = ma and went from there. τ=Fr, so the force in this case is the tension, so

τ=(mg-ma)r, and since τ= Ia, and also a = (a/r) I got eventually

a = mgr^2/(I-mr^2). Did I do this properly?

Part c. was plugging in the numbers. I was a little confused about r, r would be the radius of just the axel right? Using that, I got 20.4 cm/s^2.

I'm a little iffy on the whole thing, so hopefully I can get some help.
 
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  • #2
atm1993 said:

Homework Statement


Given the following Rdisk = 2.50 cm, Raxle = 0.250 cm, Mdisk - 25.0g, Maxle = 0.750g

a. Determine the rotational inertia of a yo-yo about it's center.
b. Dervie using force and torque the expression for the linear acceleration of a yo-yo
c. Calculate the a of the yo-yo for the given values

Homework Equations



I = (1/2)mr^2
Iα = τ

The Attempt at a Solution



Part a. pretty simple, I think I did it right. Using the moment of inertia equation for a disk, just add 2xthe I of the disks, and the I of the axle, didn't have a problem for that, got 156gcm^2.
The method is correct. Redo the numbers and if you get the same answer, you are OK here.

Part b. I wasn't completely sure if I was doing right. I started with mg-T = ma and went from there. τ=Fr, so the force in this case is the tension, so

τ=(mg-ma)r, and since τ= Ia, and also a = (a/r) I got eventually

a = mgr^2/(I-mr^2). Did I do this properly?

*** On edit ***
Not quite. Recheck the algebra.
 
Last edited:

Related to Calculating Rotational Inertia and Yo-Yo Acceleration

1. What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It depends on the mass and distribution of mass of the object and is analogous to the concept of inertia in linear motion.

2. How do you calculate rotational inertia?

The formula for calculating rotational inertia is I = Σmr², where I is the rotational inertia, Σm is the sum of the masses of all the particles in the object, and r is the distance of each particle from the axis of rotation. This formula can be used for simple objects with a known shape and uniform mass distribution.

3. What is the relationship between rotational inertia and yo-yo acceleration?

Rotational inertia and yo-yo acceleration are inversely related. This means that as the rotational inertia of a yo-yo increases, its acceleration decreases. This is because a higher rotational inertia requires more torque to produce the same angular acceleration.

4. Can you calculate rotational inertia for a yo-yo with a changing radius?

Yes, the formula for rotational inertia can be modified to account for a changing radius by using the parallel axis theorem. This theorem states that the rotational inertia of an object rotating about an axis that is parallel to its original axis of rotation is equal to the sum of its original rotational inertia and the product of its mass and the square of the distance between the two axes.

5. How does rotational inertia affect the performance of a yo-yo?

The rotational inertia of a yo-yo affects its performance in several ways. A higher rotational inertia will result in a longer spin time, as it takes more torque to slow down an object with a higher rotational inertia. It also affects the ease of performing tricks, as a yo-yo with a higher rotational inertia may be more difficult to control and maneuver.

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