Question

if particle is acted upon by a force i-2j+k N if the particle is at p(-1m,2m,3m) the torque of the force about q (3m,2m,1m) is
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Answer 1

Answer:

Torque about (0,0,0)

=rˉ×Fˉ

=(i+3k^^)×(2i+3j^^)

=3k+6(+j^)^+9(−i^)

∴TorqueaboutZaxis=coefficientofk^

=3 Nm

Answer 2

As per the data given in the above question.

We have to find the Torque of the force

Given,

$Force = \hat i-2 \hat j+\hat k$

The position vector of two points ,

$P (-1m,2m,3m) to Q (3m,2m,1m)$

Explanation:

Torque is defined as measure of the force that can cause an object to rotate about an axis.

Torque is measured in N-m

• Formula of Torque:

$τ⃗= \vec F× \vec r$

Now,

The position vector of two points (−1,2,3)m and (3,2,1)m

$\vec r = \\ [3-(-1)] \hat i + (2-2)\hat j + (1-3) \hat k$

$\vec r = 4 \hat i + 0\hat j - 2 \hat k$

Force,

$F= \hat i-2 \hat j+\hat k$

Put the value of (2) and (3) in equation (1),

$τ⃗= \vec F× \vec r$

$τ⃗= (\hat i-2 \hat j+\hat k )×(4 \hat i + 0\hat j - 2 \hat k)$

$τ⃗= |\hat i \: \: \hat j \: \: \hat k | \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: |4 \: \: 0 \: - 2| \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: |1 \: \: - 2 \: \: 1|$

$τ⃗ =\hat i[−4]−\hat j \: [6]+\hat k[−8]$

$τ⃗ = - 4\hat i−6\hat j \: - 8\hat k$

If particle is acted upon by a force i-2j+k N if the particle is at p(-1m,2m,3m) the torque of the force about q (3m,2m,1m) is -4i-6j-8k.

Project code #SPJ3