Edwin Ogie Library is a dynamic platform for education, focused on fostering mindful communication and building positive relationships by eliminating linguistic errors. Our mission is to enhance connections through thoughtful language, emotional regulation, and self-awareness, providing educational resources that inspire personal growth. We aim to promote well-being, peace, and meaningful connections, offering a space for individuals committed to refining their communication skills.
Not Everything That Stops Working Has Lost Its Value Feeling broken by life's setbacks? Discover why your value never decreases because of failure, pain, or difficult seasons. Learn the powerful lesson behind the broken machine and why your worth remains unchanged. The Broken Machine That Changed Everything Imagine walking into a workshop and finding an old industrial machine covered in dust and rust. It has not worked for years. Most people pass it without a second thought. "It is finished." "It is useless." "It belongs in the scrapyard." Those are the words many would use. Then an experienced engineer enters. Instead of seeing a useless machine, he sees possibility. He opens the casing, examines the internal parts, replaces a few worn components, reconnects the wiring, and powers it on. Within moments, the machine is running again. What changed? Not its value. Only its condition. That simple scene teaches one of the most important lessons about human...
An object is in equilibrium if it experiences no acceleration — i.e. the net force and net moment acting on it are zero. This e-book covers translational and rotational equilibrium and practical worked examples for classroom and exam preparation.
No net force — body at rest or moving with constant velocity (ΣFx = 0, ΣFy = 0).
Rotational Equilibrium
No net torque — sum of clockwise moments = sum of anticlockwise moments (ΣM = 0).
Resultant and Equilibrant Forces
The resultant is the vector sum of all forces. The equilibrant is equal in magnitude but opposite in direction to the resultant.
Parallelogram law — R² = P² + Q² + 2PQ cosθ
Example RE1: Two Forces (30 N & 40 N, θ = 60°)
Solution: R² = 30² + 40² + 2×30×40×cos60° = 900 + 1600 + 2400×0.5 = 3700 ⇒ R ≈ 60.8 N. Equilibrant = 60.8 N opposite direction.
Couples & Torque
A couple is two equal and opposite forces with parallel lines of action but not collinear — producing a pure rotation. Torque (moment) = Force × perpendicular distance (Nm)
Example CT1: Torque
50 N acting at 0.4 m produces torque = 50 × 0.4 = 20 Nm.
Equilibrium of Three Forces (Triangle of Forces)
If three forces acting at a point keep a body in equilibrium, they can be arranged to form a closed triangle.
Example TF1
Three forces are in equilibrium if the vector triangle closes (graphical or numerical check required).
Moment of a Force & Principle of Moments
Moment = Force × perpendicular distance
For equilibrium, sum of clockwise moments = sum of anticlockwise moments about any pivot.
Example MM1
A 40 N force at 0.5 m from pivot: Moment = 40 × 0.5 = 20 Nm.
Metre Rule Worked Example
Problem (i): A metre rule balances at 48 cm. A 60 g mass is at 6 cm and causes the balance point to shift to 30 cm. Find mass of the rule.
Moments about 30 cm: W×(48−30)=60×(30−6) ⇒ W×18 = 1440 ⇒ W = 80 g.
Problem (ii): Move the 60 g mass to 13 cm, find new balance point x (W=80 g).
60(x−13)=80(48−x) ⇒ 140x = 4620 ⇒ x ≈ 33 cm.
Additional Worked Examples
EQ1: Beam with two forces
A beam supported at center with 100 N and 150 N at 2 m and 3 m opposite sides — is it in equilibrium?
Clockwise 100×2 = 200 Nm, Anticlockwise 150×3 = 450 Nm ⇒ Not in equilibrium.
EQ2: Signboard with two cable tensions (vertical components)
T₁ sin40° + T₂ sin50° = 200 N. Additional data needed to find T₁ and T₂ individually.
Summary of Key Concepts
Equilibrium: No net force and no net moment.
Resultant & Equilibrant: Equilibrant balances the resultant.
Moment & Torque: Force × perpendicular distance (Nm).
Triangle of forces: Three forces in equilibrium form a closed triangle.
30-Question CBT Quiz (15 minutes)
Designed for JSS / early secondary students. Click Start Quiz to begin.
FORGIVENESS THE SECRET TO A SUCCESSFUL RELATIONSHIP Forgiveness is a critical aspect of human relationships, particularly in marriage. Treating others with mercy and leniency requires you to overlook misunderstandings and the wrongs they have done to you. The capacity to forgive is a fundamental virtue that is the linchpin of safeguarding relationships and leading a flourishing life. Lack of forgiveness causes lots of damage to marriages, and it is often the root cause of divorce in our society. It is, therefore, vital to understand that forgiveness is the key to a lasting, successful, and fulfilling marriage. Before embarking on the journey of marriage, individuals should take responsibility and learn to know themselves deeply. It is essential to realize that marriage is not a walk in the park. It requires perseverance, tenacity, and a loving spirit from the partners involved. When hurt arises, forgiveness is an indispensable tool that partners must employ to calm their difference...
Mastering the Art of Present Steps for Future Triumphs" In the pursuit of victory, every step forward is pivotal. It's essential to navigate your present position with care, for it is the springboard to your future achievements. How you handle your current endeavors directly impacts the path to your next conquests. Attempting to bypass or disregard your present circumstances can undermine your success in the steps that follow. In the realm of business, strategic maneuvering is essential to attaining your desired goals. Step into Consciousness: Harnessing Experience for Future Benefits Experience serves as our greatest teacher, guiding us towards tomorrow's rewards. Often, we fall into the trap of assuming the world revolves around us, treating our current situations with indifference and overlooking their implications for future outcomes. It's crucial to be mindful of how we approach our present steps, recognizing their significance in shaping tomorrow's victories....
EO Navigating Life’s Complexities Through Self-Consciousness A practical, story-driven guide to building mental resilience, clarity and better relationships in daily life. Expand all Collapse all Print Download .doc Introduction What is Self-Consciousness? Why it Matters The Nigerian Context Stories in Action Root Causes Upbringing & Environment Strategies to Grow Applications Exercises & Plans Scripts & Conversation Frames Resources Conclusion Introduction In a world of constant noise, stress, and social pressure, developing self-consciousness — the steady ability to notice yourself and choose — is essential. This post explains what it is, why it matters (especially in Nigeria), and how to build it with concrete stories...
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