lecture 27 relating linear and angular kinematics.pdf
DESCRIPTION
Physics; re-up only; not mineTRANSCRIPT
![Page 1: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/1.jpg)
Lecture 27: Relating Linear and Angular Kinematics
![Page 2: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/2.jpg)
Lecture Objectives 1. Relate the equations of rotational and translational quantities. 2. Apply the rotational kinematic relations in rotating objects.
![Page 3: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/3.jpg)
Relating linear and angular kinematics
3
A B
![Page 4: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/4.jpg)
Relating linear and angular kinematics
4
![Page 5: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/5.jpg)
5
Relating linear and angular kinematics
![Page 6: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/6.jpg)
Relating linear and angular kinematics
6
![Page 7: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/7.jpg)
7
Relating linear and angular kinematics
![Page 8: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/8.jpg)
Sample problem: A discus thrower moves the discus in a circle of radius 80.0cm. At a certain instant, the thrower is spinning at an angular speed of 10.0rad/s and the angular speed is increasing at 50.0rad/s2. at this instant, find the tangential and centripetal components of the acceleration of the discus and the magnitude of the acceleration.
Brown Trafton, Beijing Olympics
Given: r = 0.800m ω = 10.0rad/s α = 50.0rad/s2
![Page 9: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/9.jpg)
Given: r = 0.800m ω = 10.0rad/s α = 50.0rad/s2
For the discus moving in a circular path, the tangential and radial acceleration are:
The magnitude of the acceleration is:
![Page 10: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/10.jpg)
Sample Problem: You are asked to design an airplane propeller to turn at 2400rpm. The forward airspeed of the place is to 75.0m/s and the speed of the tips of the propeller blades through the air must not exceed 270m/s. (a) What is the maximum radius the propeller can have? (b) With this radius, what is the acceleration of the propeller tip?
![Page 11: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/11.jpg)
(a) First convert the required angular velocity ω to rad/s:
To calculate the radius we note the velocities of the plane and the tangential velocity to the velocity at the tip of the propeller:
Therefore if the velocity of the propeller blade (tip) is 75.0m/s, the radius is:
![Page 12: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/12.jpg)
(b) Using the radius r = 1.03m, the centripetal acceleration is:
While the tangential acceleration is zero because the speed is constant. ☺
![Page 13: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/13.jpg)
Seatwork
13
![Page 14: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/14.jpg)
14
Seatwork 1 to 4:
![Page 15: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/15.jpg)
15
2πrad = 1rev
![Page 16: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/16.jpg)
Seatwork answers
16
![Page 17: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/17.jpg)
17
Seatwork 1 to 4:
![Page 18: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/18.jpg)
18
Seatwork 1 to 4:
![Page 19: Lecture 27 Relating Linear and Angular Kinematics.pdf](https://reader033.vdocuments.mx/reader033/viewer/2022051316/5695d4301a28ab9b02a0995c/html5/thumbnails/19.jpg)
19
Seatwork 1 to 4: