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# Vectors and Scalars

## by Woodland Christian High School on Sep 14, 2009

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Intro to vectors and scalars for SPH3U1

Intro to vectors and scalars for SPH3U1

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## Vectors and ScalarsPresentation Transcript

• Vectors and Scalars
• Scalar – a measurement that indicates an amount without specifying direction
• Vector – a measurement that indicates both an amount and a direction
• Why is this important?
• Physics requires precision
• Distinction between the actual path of an object and the shortest path from A to B
• Where do we see vectors in physics?
• Motion – distance and displacement; speed and velocity
• Motion at constant speed (changing directions)
• Motion in two dimensions
• With or against a current or wind
• With or against gravity
• Forces – direction of a force applied to an object
• Objects speed up or slow down in the direction of the net force
• Distance and Displacement North 20 km East 15 km South 8 km West 20 km Find the distance traveled = ____ Find the displacement = ___ at ___ O
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• Option 1 – protractor (not bad)
• Option 2 – Trig (more accurate) θ Heading (bearing) is ____ – θ = _______
• Speed and Velocity South 32 km East 24 km Time = 2.5 hours North 9 km West 45 km Find the speed = ____ Find the velocity = ___ at ___ O
• θ Heading is _____ + θ = ________
• Difference between quantities
• Scalar Quantities (distance, speed)
• Indicate size only (metres, km/hr, etc)
• Measure the entire path – start to finish
• Vector Quantities (displacement, velocity)
• Indicate both size and direction (km/hr [W])
• Measure the shortest distance between the starting and ending points = “as the crow flies”
• Calculating Angles – unless the resulting angle is directly N, S, E, or W, you will
• Use trig to determine the angle from start to finish
• Convert that angle into a bearing between 0 and 360 degrees (0 = North, 180 = South, etc)
• Try these – draw and calculate
• Walk 25 m [N], then 15 m [W], then 10 m [N], then 5 m [E], finally 15 m [S]
• Find both distance AND displacement
• Drive 60 km [S], then 5 km [W], then 20 km [S], then 25 km [E], then 5 km [N] in 85 minutes
• Find both the speed and the velocity (be sure to include the heading)