Understanding R-1/R and its Equivalence

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In summary, the conversation is about the expression r-1/r! and its value. The expression r! is defined as the factorial of r, which is equal to the product of all positive integers from 1 to r. The expression r-1/r! is not equal to 1/(r-1) -1/r!, as this can be simplified to 1/(r-1)! - 1/r!. If r-1/r! is meant to be equal to r-1/r!, it cannot be further simplified. The conversation also includes a reminder to show work or thoughts when asking for help.
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Harry2
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Hey,
What is r-1/r! And sow it is equal to 1/(r-1) -1/r!
Thanks in advance.
 
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  • #2
Harry said:
What is r-1/r!
$r!$ is called the factorial of $r$ and is equal to $1\cdot2\cdot3\cdot\ldots\cdot(r-1)\cdot r$.

Harry said:
And sow it is equal to 1/(r-1) -1/r!
It is not. If you mean $\dfrac{r-1}{r!}=(r-1)/r!$, then it is equal to $\dfrac{r}{r!}-\dfrac{1}{r!}=\dfrac{1}{(r-1)!}-\dfrac{1}{r!}$ because $\dfrac{r}{r!}=\dfrac{r}{1\dots\cdot(r-1)r}=\dfrac{1}{1\dots\cdot(r-1)}=\dfrac{1}{(r-1)!}$. If you mean $r-1/r!=r-\dfrac{1}{r!}$, then it can't be further simplified.
 
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Hello Harry and welcome to MHB! :D

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FAQ: Understanding R-1/R and its Equivalence

What is R-1/R and how is it calculated?

R-1/R, also known as the Radius of Gyration, is a measure of an object's distribution of mass around an axis. It is calculated by taking the square root of the quotient of the moment of inertia and the total mass of the object.

How is R-1/R used in scientific research?

R-1/R is used in various fields of study such as physics, chemistry, and biology to understand the structural properties of molecules and materials. It can also be used to calculate the rotational kinetic energy of an object.

What is the significance of R-1/R in understanding the stability of an object?

The value of R-1/R can indicate the stability of an object. A higher value indicates a more spread out distribution of mass, which can lead to increased stability. On the other hand, a lower value can indicate a concentrated distribution of mass, which can lead to decreased stability.

How does R-1/R differ from other measures of rotational motion?

R-1/R is a measure of the distribution of mass around an axis, while other measures such as angular velocity and angular acceleration focus on the rotational speed and change in rotational speed, respectively. R-1/R provides insight into the structural properties of an object, while other measures focus on the motion of the object.

Can R-1/R be applied to both rigid and non-rigid objects?

Yes, R-1/R can be applied to both rigid and non-rigid objects. However, for non-rigid objects, the value of R-1/R may vary depending on the orientation of the object and the distribution of mass at different points in time.

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