Relative_Velocity and angular velocity,mechanics of forces

vector mechanics

1. Relative Velocity Lesson 3

2. Focus Question Does your description of motion depend on your frame of reference?

3. New Vocabulary reference frame

4. Review Vocabulary resultant: a vector that represents the sum of two other vectors; always points from the first vector’s tail to the last vector’s tip

5. Relative Motion in One Dimension A coordinate system from which motion is viewed is a reference frame. Reference frames can be stationary, such as the ground. They can also be moving, such as a bus, a plane, or a river.

6. Relative Motion in One Dimension Suppose you are walking down the aisle of a moving school bus, while your friend watches from outside. What will you see? What will your friend see?

7. Relative Motion in One Dimension Now suppose you walk towards the back of the bus. What will you see? What will your friend see?

8. Relative Motion in One Dimension Velocities can be added to determine the relative velocity: The relative velocity of object a to object c is the vector sum of object a’s velocity relative to object b and object b’s velocity relative to object c.

9. Relative Motion in Two Dimensions The method for adding relative velocities also applies to motion in two dimensions. As with one-dimensional motion, first draw a vector diagram to describe the motion and then solve the problem mathematically.

10. Relative Motion in Two Dimensions Velocity of a reference frame moving relative to the ground is v m/g .

11. Relative Motion in Two Dimensions Velocity of an object in the moving frame is v o/m .

12. Relative Motion in Two Dimensions Velocity of an object in the ground frame is v o/g .

13. Relative Motion in Two Dimensions You can use equations to solve problems for relative motion in two dimensions.

14. Use with Example Problem 4. Problem Lalei places her lunch tray on a cafeteria conveyor belt that moves westward at 0.150 m/s. With respect to the tray, a ladybug on the tray crawls northward at 0.050 m/s. What is the ladybug’s velocity with respect to the ground? Response SKETCH AND ANALYZE THE PROBLEM Sketch the situation and draw a vector diagram. List the knowns and unknowns. KNOWN UNKNOWN v l/t = 0.050 m/s north v l/g = ? v t/g = 0.150 m/s west SOLVE FOR THE UNKNOWN Add the velocities together. Because v l/t and v t/g are perpendicular, use the Pythagorean theorem to add their magnitudes. N v l/t v t/g v l/g θ

15. EVALUATE THE ANSWER The units are correct; velocity is in meters per second. The direction agrees with our vector diagram. Use with Example Problem 4. Problem Lalei places her lunch tray on a cafeteria conveyor belt that moves westward at 0.150 m/s. With respect to the tray, a ladybug on the tray crawls northward at 0.050 m/s. What is the ladybug’s velocity with respect to the ground? Response SKETCH AND ANALYZE THE PROBLEM Sketch the situation and draw a vector diagram. List the knowns and unknowns. KNOWN UNKNOWN v l/t = 0.050 m/s north v l/g = ? v t/g = 0.150 m/s west SOLVE FOR THE UNKNOWN Use trigonometry to find the direction of the velocity. N v l/t v t/g v l/g θ

16. Quiz Subtract the velocities. D Add the velocities. C Average the velocities. B Add the squares of the velocities. A When both an object and the reference frame it moves in move in the same direction, how do you find the velocity of the object relative to the ground? 1. CORRECT

17. Quiz Add the velocities. D Subtract the velocities. B Average the velocities. C Add the squares of the velocities. A When both an object and the reference frame it moves in move in opposite directions, how do you find the velocity of the object relative to the ground? 2. CORRECT

18. Quiz v b/c + v c/b = v a/c D v a/b + v b/c = v a/c B v a/c + v b/c = v a/b C v a/c + v a/b = v b/c A Object a moves relative to object b, and object b moves relative to object c. Which equation shows the correct way to find the relative velocity of object a to object c? 3. CORRECT

19. Quiz 7.0 m/s north D 7.0 m/s south C 13.0 m/s north B 13.0 m/s south A A boat is moving north at 10.0 m/s relative to the shore. If you walk toward the back of the boat at 3.0 m/s relative to the boat, what is your velocity relative to the shore? 4. CORRECT

20. Quiz Subtract the magnitudes and use the direction of the longer vector. D Add the magnitudes and use the direction of the longer vector. C Place the position vectors tip-to-tail. B Place the velocity vectors tip-to-tail. A How do you find the resultant velocity vector when solving a problem involving motion in two dimensions? 5. CORRECT