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Kinematics

Kinematics. Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Motion can be described using many words such as fast, slow, speeding up, turning, etc. In physics we use mathematical quantities to describe motion

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Kinematics

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  1. Kinematics

  2. Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations

  3. Motion can be described using many words such as fast, slow, speeding up, turning, etc. • In physics we use mathematical quantities to describe motion • The mathematical quantities that are used to describe the motion of objects can be divided into two categories. The quantity is either a vector or a scalar

  4. Scalars are quantities that are fully described by a magnitude (or numerical value) alone. • Vectors are quantities that are fully described by both a magnitude and a direction.

  5. Let’s see the difference between scalar and vector quantities: • 5m – 5 metres only gives a magnitude, NOT a direction, therefore it is a scalar quantity • 30m/s, east – this gives a magnitude AND a direction • 4000 calories – What is this? Scalar or vector? • 22 km north - ??

  6. Scalar quantities include such things as mass, time, distance, speed, work, and energy • Position, displacement, velocity, acceleration, force, weight, and momentum are examples of vector quantities

  7. Vectors • Since vectors describe the magnitude and the direction we use arrows to signify the direction • The direction of a vector is stated using square brackets behind its magnitude. (i.e., 12 km [N])

  8. Vectors • The length of the arrow represents the magnitude of the displacement • The tail of a vector is called the origin and the tip is called the terminal point • Vectors are written with an arrow above them, i.e A = 750m, due east

  9. Addition and Subtraction of Vectors • Many times two or more vectors will need to be added together • The simplest situation occurs when the two vectors point along the same direction – This is known as COLINEAR • Let’s look at an example!

  10. A B • Start Finish R

  11. Let’s say that a car travels along a straight line with a displacement vector A of 275m, due east • The car then moves again in the same direction with a vector B of 125m due east • Added together, the two vectors give the vector of R • This total vector is known as the resultant vector • Notice that the tail of the first vector is lined up next to the head of the second vector

  12. Because the two vectors point in the same direction and are oriented tail to head, they can simply be added together • Therefore R = A + B • = 400m, due east

  13. Addition and Subtraction • Sometimes you will encounter perpendicular vectors that need to be added together B • A

  14. You could imagine that a car traveled 275m due east with a vector of A . The car then traveled 125m due north with a vector of B • The resultant vector is R • R B • A

  15. Notice again that the vectors are arranged in a tail to head fashion • However since the vectors do not point in the same direction we must use Pythagorean theorem • The magnitude of R = √ (275m)2 + (125m)2 = 302m

  16. Now we have found the magnitude, but if we want to solve the resultant vector we also need to find a direction! • We need to work with what we are given! We know the values of the sides A and B

  17. Therefore • Θ = tan-1 (B/A) = (125m/275m) = 24.4˚ • Therefore the resultant displacement of the car is 302m and points north east at 24.4˚

  18. Subtraction of Vectors • When a vector is multiplied by -1 the magnitude of the vector remains the same but the direction of the vector is reversed • Lets consider an example: • A woman climbs 1.2 m up a ladder. Her displacement vector D is 1.2m upwards • However her displacement vector for climbing 1.2m down the ladder is -D

  19. More Subtraction • C= A + B B • A

  20. We can find A by = C – B • OR we can write the equation as A = C + (-B) • NOTICE that vectors C and B are arranged tail to head, hence they can be added together

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