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Topple

Usually, due to friction, a torque is applied on a body opposing the change of motion and usually due to the quick axis of rotation shifts, if the momentary axis of rotation falls outside the body that time the body topples and this is the condition of toppling. When a torque is applied to a body the instantaneous axis of rotation shifts. The body topples if the instantaneous axis of rotation falls outside the body.

A gyroscope is a device consisting of a wheel or circle mounted with the goal that it can turn quickly about an axis which is itself allowed to change in course. The direction of the axis isn’t impacted by shifting of the mounting, so the gyroscope can be utilized to give soundness or keep a reference bearing in route framework, and stabilizers.

Conditions of Toppling:

  1. A block is resting on a slope, and the angle is increased until toppling occurs. The angle is the limiting frictional force not yet reached and so the block has not begun to slide. The weight of the block is taken vertically through its center of mass and the resultant and the frictional force must act between ends of the block. The overall contact force must be vertical. When the net moment of force is non zero that time the toppling occurs. To reduce it (topple) the weight of the block must be vertical.
    When the center of mass passes through the lowest corner of the block that is the critical point. The relation between the angle of slope and block dimension is tan θ =a/b. If b is increased the block topple easily since tan tan θ is reduced b is increased.
  2. Exercise on Sliding and Toppling

Beads rest on table whose mass is m and the force P, length of the block are  2x, height is x and the friction coefficient is μ.

  • If the block is on a sliding point

Condition for toppling before sliding

A gradually expanding even force is applied to one vertical face. On the off chance that this power is applied close to the lower part of the face, as the force increases the square or a block will slide before it overturns. On the off chance that the force is applied close to the top, the block topples before it begins to slide.

How to solve problems based on the toppling effect

A horizontal force F is applied a cubical block of mass m and side L rests with a coefficient of friction on a rough surface. If the coefficient of friction is high then find the minimum required force to topple to the block.

When force is minimum

F=μN

N=mg

∴F=μmg

When Force is maximum 

∑M=0

∴∑M=∑F.d

0=F×L – mg×L/2

∴F=mg/2

Conclusion:

When the weight force acts outside the base of the object the topple occurs. The failure of the toppling deformation is bent towards the free direction and gradually develops into the slope under the combined forces of gravity and groundwater pressure, and so on. 

When an object stands on a surface there are 2 forces acting on it: 

  1. Weight of an object 
  2. Resultant of contact forces.

When the object is on the toppling then the equilibrium of an object is broken. When a force acts outside the base of the object that time toppling occurs. The contact force is usually paralleled to the sliding surface and normal contact is perpendicular to the sliding surface.