Rotational and translational motion confusion If I had a rigid body, such as a wardrobe, so that its centre of mass is above the ground and I tilt it slightly. I have read that the normal force of the floor on the wardrobe must be equal and opposite to the weight of the object as we have no translational motion. However if I let the wardrobe topple over, its centre of mass is now lower. How can the centre of mass have changed positions if the normal force and weight are equal and opposite to oppose any translational motion?
 A: During the tipping, the weight of the wardrobe is actually lower. You know the weight was lower because its centre of mass moved down and the weight is exactly equal to the normal force exerted by the floor. This is a circular definition and pretty useless, but I will get there in a second.
There are two definitions of weight: you can measure weight as the force exerted by gravity, or simply $m\cdot g$, but you can also define weight as the mass as measured by a scale multiplied by $g$.
This second definintion is often used in Newtonion physics and is equal to the normal force. To understand the normal force better you must remember that the normal is caused by atoms in the floor repelling the atoms of some other object (in this case the wardrobe). Gravity tries to pull the wardrobe into the floor but as the atoms of the wardrobe get near the atoms of the floor the normal force grows quickly. In fact, so quickly that you can consider objects as solid and the normal force as instantaneous.
To get a better grasp, imagine the wardrobe is on a scale inside of a very high elevator. If the elevator is in freefall the normal force is zero because the wardrobe and elevator move at the same speed and the wardrobe doesn't get pushed into the ground. If you slow deceleratethe elevator using cables the normal force increases to the point that the elevator stops moving, at which point the normal force is equal to $mg$. Extending this, the weight can also be greater than the force of gravity if you accelerate the elevator upwards. You have probably felt this already when you were inside an elevator.
In conclusion the weight of an object (using the normal force definition) depends on the relative acceleration between the floor and the object and so can vary if the object is falling.
