Toppling and Step Climbing
At the threshold of toppling, the normal reaction shifts to the edge that becomes the pivot and moments about that edge determine the required force; step-climbing analysis similarly uses the corner contact as instantaneous pivot.
Why this shows up in the exam
Pushing blocks without toppling · Wheels climbing curbs or steps · Finding critical force application height
Learn the idea
Impending toppling or step climbing is determined by torque balance about the active contact edge. Impending toppling or step climbing is determined by torque balance about the active contact edge. Start from a clear axis, origin, body, and reference frame; the geometry and constraints then decide which rotational law is safe to use.
🧠 Memory hook: At tipping, the support shrinks to one edge.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum tau_edge = 0 — Threshold moment balance about the impending pivot edge.
- F d_F = M g d_g — Generic balance between applied-force and weight lever arms.
How to approach it
- 1Identify the contact about to lift
- 2Take moments about that edge or corner
- 3Compare toppling and sliding thresholds
Common slip-ups that cost marks
- •Taking moments about the centre instead of the impending edge
- •Keeping a nonzero reaction at the lifted contact
- •Ignoring simultaneous sliding threshold
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Masses 1 kg and 3 kg lie at x = 0 and x = 4 m. Find the x-coordinate of their centre of mass.
More from Motion of System of Particles and Rigid Body
Conservation of momentum and angular momentum
The total linear and angular momentum of a system remains constant in the absence of external forces or torques, including during collisions and rotational motion.
Moment of inertia and radius of gyration
Moment of inertia quantifies how mass is distributed with respect to an axis of rotation, and the radius of gyration is a measure related to this distribution.
Torque and rotational equilibrium
Torque is the rotational analogue of force, causing angular acceleration, and equilibrium occurs when the net torque on a body is zero.
Center of mass: definition and calculation
The center of mass is the point representing the mean position of the mass in a system, and can be calculated for discrete particles or continuous bodies.
Rotational kinematics and dynamics
Rotational kinematics describes the motion of rotating bodies, while dynamics relates torque, angular acceleration, and rotational kinetic energy.
Centre of Mass of Discrete Particles
For discrete particles, the centre-of-mass position is the vector sum of each mass times its position divided by total mass; this point governs translation even when the particles move relative to one another.