Thus the torque due to normal force is in clockwise direction.

Torque of Normal Force on a Cubical Block Sliding down an Inclined Plane

When a cubical block of mass m and edge a slides down a rough inclined plane with an inclination angle theta, it experiences various forces acting on it. One of these forces is the normal force, which acts perpendicular to the plane of contact between the block and the inclined plane. To find the torque of the normal force acting on the block about its center, we need to understand the concept of torque and its calculation.

1. Torque:
Torque is the rotational equivalent of force. It is the tendency of a force to rotate an object about an axis. Mathematically, torque is defined as the product of the force applied and the perpendicular distance from the axis of rotation to the line of action of the force.

2. Torque of a Force:
The torque (T) of a force (F) about a point or axis of rotation can be calculated using the formula:
T = F * r * sin(theta)

Where:
T is the torque,
F is the applied force,
r is the perpendicular distance from the axis of rotation to the line of action of the force,
theta is the angle between the force vector and the line joining the point of rotation and the point of application of the force.

3. Torque of Normal Force:
In the case of the cubical block sliding down the inclined plane, the normal force acts perpendicular to the plane of contact. Therefore, the angle (theta) between the normal force vector and the line joining the center of the block and the point of application of the force is 90 degrees.

Since sin(90) = 1, the torque of the normal force can be simplified to:
T = F * r

4. Determining the Force and Perpendicular Distance:
To calculate the torque of the normal force, we need to determine the force (F) and the perpendicular distance (r).

- The normal force (N) can be determined using the equation N = mg * cos(theta), where m is the mass of the block, g is the acceleration due to gravity, and theta is the inclination angle of the inclined plane.

- The perpendicular distance (r) can be determined as half the length of the diagonal of the cube. Using the Pythagorean theorem, r = (a * sqrt(2)) / 2, where a is the edge length of the cube.

5. Calculating the Torque:
Substituting the values of F and r into the torque equation, we get:
T = (mg * cos(theta)) * ((a * sqrt(2)) / 2)

Conclusion:
The torque of the normal force acting on the cubical block about its center is given by the equation:
T = (mg * cos(theta)) * ((a * sqrt(2)) / 2)

This torque represents the rotational tendency caused by the normal force as the block slides down the rough inclined plane with uniform speed.

Mg and mgcos(theta) pass through the centre so they produce zero torque about the centre. But mgsin(theta) will produce torque which is equal to 1/2mgasin(theta)