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Understanding Human Behaviour Without Spoken Words

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Understanding Human Behaviour Without Spoken Words — Edwin Ogie Library Understanding Human Behaviour Without Spoken Words Nonverbal Communication as a core human skill — simple, practical, and classroom-friendly. Chapter Objectives Introduction Meaning & Scope Major Channels Interpreting Behaviour Culture & Ethics Practical Applications Case Illustrations Reflection & Practice Summary & Terms By Edwin Ogie Library — clear, usable lessons for students and teachers. Chapter Objectives At the end of this chapter, the reader should be able to: Clearly define nonverbal communication and explain its role in human interaction. Identify and interpret major forms of nonverbal behaviour with accuracy. Analyse behaviour using clusters of cues rather than isolated signals. Apply nonverbal awareness eff...
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Motion in a Circle

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Lesson Note: Motion in a Circle

Motion in a Circle

Objectives:

  1. Establish expressions for angular velocity, angular acceleration, and centripetal force.
  2. Solve numerical problems involving motion in a circle.
  3. Interpret the applications of circular motion in real life.

Key Concepts and Formulas

Angular Velocity (ω): ω = Δθ/Δt, where Δθ is the angular displacement (in radians) and Δt is the time interval.

Angular Acceleration (α): α = Δω/Δt, where Δω is the change in angular velocity over time Δt.

Centripetal Force (Fc): Fc = mω²r = mv²/r, where m is mass, ω is angular velocity, r is the radius, and v is linear velocity.

Centrifugal Force: This is a fictitious force experienced in a rotating frame; it has the same magnitude as the centripetal force (mω²r) but acts outward.

Applications: These formulas are applied in designing rotating machinery, understanding planetary motion, and analyzing vehicles on curved paths.

Worked Examples

The following 6 worked examples (in green boxes) illustrate the application of the formulas for motion in a circle.

Example 1:
A wheel rotates through 6.28 radians in 2 seconds. Find its angular velocity.
Solution: ω = Δθ/Δt = 6.28/2 = 3.14 rad/s.

Example 2:
The angular velocity of a rotating disc increases from 2 rad/s to 8 rad/s in 3 seconds. Find the angular acceleration.
Solution: α = Δω/Δt = (8 - 2)/3 = 6/3 = 2 rad/s².

Example 3:
A 5 kg object is attached to a string and rotates in a circle of radius 0.8 m with an angular velocity of 4 rad/s. Find the centripetal force.
Solution: Fc = mω²r = 5×(4²)×0.8 = 5×16×0.8 = 64 N.

Example 4:
A car of mass 1200 kg turns along a curve of radius 50 m at a speed of 20 m/s. Calculate the centripetal force acting on it.
Solution: Fc = mv²/r = 1200×(20²)/50 = 1200×400/50 = 9600 N.

Example 5:
A merry-go-round completes 5 revolutions in 10 seconds. Find its angular velocity (Note: 1 revolution = 2π radians).
Solution: Total angle = 5×2π = 10π rad; ω = 10π/10 = π rad/s.

Example 6:
In a collision problem, a 1500 kg car moving at 15 m/s collides inelastically with a 1000 kg car at 10 m/s (in the same direction). Find the final velocity using conservation of momentum.
Solution: (1500×15 + 1000×10) = (2500)v' → v' = (22500 + 10000) / 2500 = 32500/2500 = 13 m/s.

JAMB CBT Quiz on Motion in a Circle

Total time: 900 seconds

This lesson covers: Angular velocity: ω = Δθ/Δt Angular acceleration: α = Δω/Δt Centripetal force: F₍c₎ = mω²r = mv²/r Centrifugal force (fictitious): mω²r Applications in circular motion and collisions. The worked examples illustrate numerical problems and real-life applications such as calculating angular velocity, acceleration, centripetal force, and solving collision problems.

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