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Speed, Velocity, and Acceleration in Linear & Rotational Systems

Learn how to calculate and measure speed, velocity, and acceleration in linear and rotational systems, including concepts like displacement, angular speed, and angular acceleration. Practice exercises included for comprehensive understanding.

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Speed, Velocity, and Acceleration in Linear & Rotational Systems

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  1. Speed, Velocity And Acceleration EQs 11-12

  2. EQ 11 - Speed • EQ 11-How would you calculate and measure speed and velocity in linear and rotational systems? • Speed – ratio of distance traveled to time spent traveling, d/t or slope (rise/run) on a time and distance graph. See p123 Table & Figure 3.1

  3. EQ 11 – Velocity 1 • Round trip & constant vs. average vs instantaneous speed • Speed or vave= d/t; p125 Ex 3.1 • PRACTICE! p.136 #2 & 6 • Velocity – same as speed but use displacement instead of distance. What’s displacement?

  4. EQ 11 – Velocity 2 • Displacement’s a vector, distance between 2 points in a direction. • Plain distance is scalar because it has magnitude or size without direction. • vave = Δd/t Here, v & d are in bold! See p.127 Ex 3.2 • PRACTICE!p.136 #8d

  5. EQ 12 – Acceleration 1 • EQ 12-How would you calculate and measure acceleration in linear and rotational systems? • acceleration – rate of change of object’s velocity: • aave = Δv/t

  6. EQ 12 – Acceleration 2 • This happens when you change speed, direction or both. • See Table 3.2 on p128 & Figures 3.5-3.6 on p129. • See Ex 3.3 on p130. • PRACTICE! Motion Lab & p137#13 • deceleration – object is slowing down so negative aave

  7. Angular Speed & Acceleration EQs 11-12

  8. EQ 11– Angular Speed 1 • EQ 11-How would you calculate and measure angular speed, i.e., speed in rotational systems? • Angular speed (ω) – angular displacement in radians (Δθ) divided by time change (Δt).

  9. EQ 11– Angular Speed 2 • Degrees must be in radians; so, use 1 revolution=360˚=2π radians to convert. • ω = Δθ / Δt • Speed of point on circle is distance (r) of point from center times angular speed (ω)

  10. EQ 11– Angular Speed 3 • v = r ω • See p131-133 & Examples 3.4-3.5 • PRACTICE! p.137 #10-11 & 15

  11. EQ 12 – Angular Acceleration 1 • EQ 12-How would you calculate & measure angular acceleration in rotational systems? • Angular acceleration – change in angular speed divided by related change in time • α = Δ ω / Δ t

  12. EQ 12 – Angular Acceleration 2 • See p. Example

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