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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

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Motion in a Circle

Newton’s Laws and Circular Motion

Objectives:

  1. Establish expressions for angular velocity, angular acceleration, and centripetal force.
  2. Solve numerical problems involving motion in a circle.
  3. Interpret the area under a force–time graph in terms of impulse.
  4. Deduce the relationship between linear speed and angular speed.
  5. Apply concepts of circular motion in collisions (elastic and inelastic) where applicable.

Key Formulas and Concepts

Angular Displacement: θ = S / R
(θ in radians, S = arc length, R = radius)

Angular Velocity: ω = θ / t
(ω in radians per second)

Relationship between Linear Speed and Angular Speed:
S = R * θ so that v = S / t = R * (θ / t) = ω * R
v = ω * R

Angular Acceleration: α = Δω / t
(α in radians per second squared)

Centripetal Force: Fc = m * v² / R = m * ω² * R
(Force required to keep an object moving in a circle)

Centrifugal Force: A perceived force acting outward on a body moving in a circle; not a real force but an effect of inertia in a rotating reference frame.

Worked Examples

The following 6 worked examples (each in a green box) illustrate the application of the above formulas and concepts.

Example 1: A stone tied to a string moves in a circle of radius 2 m. If its angular velocity is 4 rad/s, find its linear speed.
Solution: v = ω * R = 4 * 2 = 8 m/s.

Example 2: A wheel rotates with an angular displacement of 6 radians in 2 s. Calculate its angular velocity.
Solution: ω = θ / t = 6/2 = 3 rad/s.

Example 3: A car of mass 1000 kg is moving in a circular track of radius 50 m at 20 m/s. Determine the centripetal force acting on the car.
Solution: Fc = m * v² / R = 1000 * (20²)/50 = 1000 * 400/50 = 8000 N.

Example 4: A merry-go-round accelerates from rest to an angular velocity of 2 rad/s in 5 s. Find its angular acceleration.
Solution: α = Δω / t = 2/5 = 0.4 rad/s².

Example 5: A cyclist travels around a circular track of radius 30 m at a constant speed of 12 m/s. Calculate the angular velocity of the cyclist.
Solution: ω = v / R = 12/30 = 0.4 rad/s.

Example 6: In a collision problem, a 2 kg ball moving at 3 m/s strikes a stationary 3 kg ball elastically. Using conservation of momentum and kinetic energy, the final velocities can be computed (detailed steps omitted here for brevity).
Note: For elastic collisions, use:
v₁' = [(m₁ - m₂)/(m₁ + m₂)]v₁ + [2m₂/(m₁ + m₂)]v₂ and v₂' = [2m₁/(m₁ + m₂)]v₁ + [(m₂ - m₁)/(m₁ + m₂)]v₂.

JAMB CBT Quiz on Motion in a Circle

Total time: 900 seconds

This lesson covers: Angular velocity (ω = θ/t) and angular acceleration (α = Δω/t) Relationship between linear speed and angular speed: v = ω * R Centripetal force: F₍c₎ = m * v² / R = m * ω² * R Angular displacement: θ = S / R Collision formulas for elastic and inelastic collisions (momentum conservation and, for elastic collisions, kinetic energy conservation) The worked examples illustrate numerical problems and real-life applications of circular motion.

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