## Thursday, January 14, 2016

### Need for Torque in Rotational Dynamics and Direction of Torque

Torque means the turning effect and we need to use this to understand rotational motion. To put any body in rotational motion, we not only need to apply the force and we also need to apply the force on the body but it shall be away from the axis of rotation. If a force is applied on the axis of rotation, it cannot produce rotational motion in the body. Torque is defined as the cross product of force and displacement. It means torque is the vector product of force and displacement and we do get the result also a vector quantity having both magnitude and direction.

When we find the cross product of force and displacement, we get it as the product of force and perpendicular distance of the point of action of force from the axis of rotation.

We shall apply torque on any body to put it in rotational motion. As the applied force produce displacement and give translatory motion in the body, applied torque on the body produces rotational motion in the body.

We do provide handle to a door at the edge of the door quite far from axis of rotation. This provides more distance to the applied force on the door and hence provides more torque on the body. This makes opening the door easy task. That is the reason why we always see the opening handler of door is always at the edge of the door never at the starting point from the axis of rotation.

This is explained in detail in the video below.

Finding the direction of Torque

We can also find the direction of the torque using a rule called cork screw rule or right hand thumb rule. As the torque is a vector product of force and displacement, it shall have both magnitude and direction. We can find the magnitude using the vector cross product magnitude and to find the direction, we shall use cork screw rule.

As per this rule, if we rotate the head of the screw from the direction of force to the direction of displacement, we can get the direction of the torque as the direction of the advancement of the tip of the nail.

If we rotate the head of the screw in the direction from displacement to force, we get the torque again in the direction of the tip of the screw but in the down ward direction in the perpendicular plane.

It can be noticed that the cross product of two vectors does not satisfy commutative rule.The magnitude of the product is same but the direction is opposite to each other.

It can also be noticed that the force and displacement are in one plane and the cross product of the two torque is in the perpendicular plane. Hence the dot product of torque and force or displacement is zero. It is simply because they have an angular separation of ninety degree and hence their dot product is zero.

It is demonstrated in the following video in detail as shown below.

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