1. Have you ever used Mathematica?

2. What do we want to do today?! Thursday: 10-1-1440
A bit of housekeeping
Chapter-4
Prof. Zain Yamani
Office: / 3102; Phone: ; Mobile:
HP:

3. A bit of housekeeping
Attendance
If you come late, please make me aware during the (end of) the same lecture.

4. A bit of housekeeping
Office Hours in term 181

5. A bit of housekeeping
The Rotation Matrix!!
B = {-2Sqrt[3], -2} with rotation q = p/6
Check with Mathematica!!
We can do nice things with Mathematics for rotation 

6. Chapter-4: Motion in Two and Three Dimensions
Position, displacement, velocity and acceleration
Projectile motion
Uniform Circular Motion
Relative Motion in 1 D
Relative Motion in 2 D

7. Ch-4 2D & 3D motion This is in rectangular coordinates
r(t) = x(t) i + y(t) j + z(t) k
This is in rectangular coordinates
v(t) = vx(t) i + vy(t) j + vz(t) k
a(t) = ax(t) i + ay(t) j + az(t) k
What does 2D & 3D motion with constant acceleration mean?

8. Ch-4
2D & 3D motion
What about in other coordinates, like for example polar coordinates or spherical polar coordinates?
v(t) =
a(t) =

9. Ch-4 Projectile Motion What do we mean by projectile motion?
How do we deal with projectile motion problems?
Mathematica: projectile motion

10. Projectile motion
A driver wants to make his car jump over 8 cars parked at 1.5 m below a horizontal ramp as shown in Figure 2. The horizontal distance he must clear without hitting any of the parked cars is 22 m. If the initial takeoff angle of the car is 7.0ᴼ above the horizontal ramp, then what should be the car’s initial minimum speed so that the driver can land without hitting any of the parked cars?
A) 24 m/s
B) 40 m/s
C) 32 m/s
D) 20 m/s
E) 28 m/s
152-1

11. What if we had air resistance (drag)?
Mathematica: projectile air resistance

12. Uniform Circular Motion
Ch-4
Uniform Circular Motion
What do we mean by uniform circular motion?
How do we deal with uniform circular motion problems?

13. A problem on Uniform Circular Motion
A particle is in a uniform circular motion in counter clockwise direction starting from the positive x-axis. Its period of motion is 2.1 s and the magnitude of its radial acceleration is 3.0 m/s2. Determine the velocity of the particle when it exactly completes 1.5 revolutions.
152-1

14. A problem on Uniform Circular Motion
A particle is in a uniform circular motion in counter clockwise direction starting from the positive x-axis. Its period of motion is 2.1 s and the magnitude of its radial acceleration is 3.0 m/s2. Determine the velocity of the particle when it exactly completes 1.5 revolutions.
152-1

15. Another problem on Uniform Circular Motion
A star with a diameter of 40.0 km rotates about its central axis making two revolutions per second. What is the speed (km/s), of an object on the star’s equator?
A) 251
B) 628
C) 400
D) 100
E) 450
141-1

16. Ch-4 Relative Motion What do we mean by relative motion (1-D)?
How do we deal with uniform circular motion problems?

17. A problem on Relative Motion
Snow is falling vertically at a constant speed of 7.0 m/s. At what angle from the vertical direction do the snowflakes appear to be falling as viewed by the driver of a car travelling on a straight, level road with a speed of 16 m/s?
A) 66ᴼ
B) 45ᴼ
C) 13ᴼ
D) 52ᴼ
E) 81ᴼ
152-1

18. Another problem on Relative Motion
A boat is traveling upstream towards the east at 10 km/h with respect to the water of a river. The water is flowing at 5.0 km/h with respect to the ground. A man on the boat walks from front to rear at 3.0 km/h with respect to the boat. What are the magnitude and direction of the man’s velocity with respect to the ground?
A) 2.0 km/h, towards the east
B) 2.0 km/h, towards the west
C) 8.0 km/h, towards the east
D) 12 km/h, towards the east
E) 18 km/h, towards the west
141-1

19. Another problem on Relative Motion
A boat is traveling upstream towards the east at 10 km/h with respect to the water of a river. The water is flowing at 5.0 km/h with respect to the ground. A man on the boat walks from front to rear at 3.0 km/h with respect to the boat. What are the magnitude and direction of the man’s velocity with respect to the ground?
A) 2.0 km/h, towards the east
B) 2.0 km/h, towards the west
C) 8.0 km/h, towards the east
D) 12 km/h, towards the east
E) 18 km/h, towards the west
141-1

20. Chapter-4 slides 

21. Mathematica can choose 

22. !!Check official Phys-101 website!!