Question

If $bold F with bold rightwards arrow on top$ is the force acting on a particle having position vector $straight r with rightwards arrow on top space a n d space tau with rightwards arrow on top$ be the the torque of this force about the origin, then

$straight r with rightwards arrow on top. straight tau with rightwards arrow on top space not equal to space 0 space and space bold F with bold rightwards arrow on top space. space straight tau with rightwards arrow on top space equals space 0$
$straight r with rightwards arrow on top. straight tau with rightwards arrow on top space greater than space space 0 space and space bold F with bold rightwards arrow on top space. space straight tau with rightwards arrow on top space less than space 0$
$straight r with rightwards arrow on top. straight tau with rightwards arrow on top space equals space space 0 space and space bold F with bold rightwards arrow on top space. space straight tau with rightwards arrow on top space equals space 0$
$straight r with rightwards arrow on top. straight tau with rightwards arrow on top space equals space space 0 space and space bold F with bold rightwards arrow on top space. space straight tau with rightwards arrow on top space not equal to space 0$

Solution

straight r with rightwards arrow on top. straight tau with rightwards arrow on top space equals space space 0 space and space bold F with bold rightwards arrow on top space. space straight tau with rightwards arrow on top space equals space 0

Torque is an axial vector ie, its direction is always perpendicular to the plane containing vectors $straight r with rightwards arrow on top space a n d space F with rightwards arrow on top$
$stack straight tau space equals with rightwards arrow on top space bold r with bold rightwards arrow on top bold space bold x bold space bold F with bold rightwards arrow on top bold space Torque space is space perpendicular space to space both space bold r with bold rightwards arrow on top space and space bold F with bold rightwards arrow on top therefore comma straight tau with rightwards arrow on top. bold r with bold rightwards arrow on top space equals space 0 stack straight F. space with rightwards arrow on top straight tau with rightwards arrow on top space equals space 0$

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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Give one example of tensor.

What is module of vector?

What are equal vectors?

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