Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

give proof for the query in the subject

give proof for the query in the subject

Grade:

2 Answers

mohit sengar
39 Points
10 years ago

Couple is a system of forces with a resultant moment but no resultant force. Another term for a couple is a pure moment. Its effect is to create rotation without translation, or more generally without any acceleration of the centre of mass.as its does not move the centre of mass that's why the the moment of force produced by a couple is same about every point.

mohit sengar
39 Points
10 years ago

The proof of this claim is as follows: Suppose there are a set of force vectors F1F2, etc. that form a couple, with position vectors (about some origin Pr1r2, etc., respectively. The moment about P is

M = \mathbf{r}_1\times \mathbf{F}_1 + \mathbf{r}_2\times \mathbf{F}_2 + \cdots

Now we pick a new reference point P' that differs from P by the vector r. The new moment is

M' = (\mathbf{r}_1+\mathbf{r})\times \mathbf{F}_1 + (\mathbf{r}_2+\mathbf{r})\times \mathbf{F}_2 + \cdots

We can simplify this as follows:

M' = \mathbf{r}_1\times \mathbf{F}_1+\mathbf{r}\times \mathbf{F}_1 + \mathbf{r}_2\times \mathbf{F}_2+\mathbf{r}\times \mathbf{F}_2 + \cdots
M' = \left(\mathbf{r}_1\times \mathbf{F}_1 + \mathbf{r}_2\times \mathbf{F}_2 + \cdots\right) + \mathbf{r}\times \left(\mathbf{F}_1 + \mathbf{F}_2 + \cdots \right)

The definition of a force couple means that

\mathbf{F}_1 + \mathbf{F}_2 + \cdots = 0

Therefore,

M' = \mathbf{r}_1\times \mathbf{F}_1 + \mathbf{r}_2\times \mathbf{F}_2 + \cdots = M

This proves that the moment is independent of reference point. 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free