Rotational Motion Basics

1. State the rotational equivalents of the linear quantities

   Linear	Rotational
   mass, linear inertia...m	moment of inertia........I
   displacement............x	angle..........................q
   velocity.....................v = Dx /Dt	angular velocity..........w = Dq /Dt
   acceleration.............a = Dv /Dt	angular acceleration...a = Dw /Dt
   force.........................F	torque.........................t

2. Indicate which rotational quantities are vectors and which are scalars.

3. State that, by using the right hand thumb rule, rotational vectors can be represented as arrows where the length is proportional to the magnitude and the arrow head represents the direction.

4. By looking at the arrows representing rotational velocity and acceleration, determine if an object's rotation is speeding up or slowing down.

speeding up: directions match

slowing down: directions are opposites

5. Convert between various methods of expressing rotational velocities. ω, RPS, RPM (note: RPS can also be called angular frequency). Relevance: of the 3 expressions, RPM rating will be found on any motor or machine that rotates. RPM is key to the performance of any of these real-world devices.

Homefun (formative/summative assessment): Read sections 8.1, find an electrical device that rotates such as a motor or fan and record the number. Is it evenly divisible by 60?

Formative Assessment: Physics Investigation

Follow up Questions

Linking Rotation to Linear Motion

6. Given the equations in objective 1, calculate w and a .

   clock problems

   fan problems

7. State the 3 equations that link the linear world to the rotational world.

x = rq

v = rw

a = ra

8. Use the link equations to solve problems.

   linear velocity of a rolling wheel

   wishing well problem

   belt drive problem

Homefun (formative/summative assessment): Read section 8.2, do Section Review Problems 5, 7, 9 p. 200.

Torque

9. Calculate torque.

t = F x r

t = F r sinq

10. Find net torque for various situations with multiple torques.

seesaw

pullies

Homefun (formative/summative assessment): problems 14, 15 p. 203; 16, 17, 18 p. 205

The Moment of Inertia--Rotational Inertia

11. Define moment of inertia. The resistance to a change in rotational velocity.

12. State that moment of inertia does not depend on gravity. For example, a sledge hammer will still be hard to swing even in outer space.

13. Solve problems using the equation for the moment of inertia of a rotating point source of mass. I = m(r^2)

14. Explain in general terms why different objects with the same mass can have different moments of inertia.

15. State that an object with the same mass and same diameter but lower moment of inertia will roll down a slope in less time than one with a higher moment of inertia.

16. Given two or more objects with the same mass, estimate which one will have the highest moment of inertia.

Homefun (formative/summative assessment): problems 21, 22, 23, challenge problem, page 208

Newton's Second Law for Rotational Motion

17. State Newton's second law for Rotation both in words and mathematically.

    t = I a

18. Sole problems using Newton's second law for rotation

Homefun (formative/summative assessment): problems 27, 29 page 210

Center of Mass

Relevance: Center of mass is a key issue in sports such as gymnastics, figure skating, and diving. It is a major issue in most forms of martial arts.

19. Describe how a thrown object will rotate.

20. Describe how to find the center of mass of an object.

21. Describe the conditions that cause an object to tip over.

22. State the differences between stable, unstable and neutral equilibrium.

23. Describe how forces applied to different locations relative to te center of mass can produce translation and/or rotation.

Review of Objectives 1- 13 (1-3 days)

Formative Assessments:

1. Work review problems at the board

2. Work practice problems.

Metacognition Problem Solving Question: Can I still work the problems done in class, several hours or days later? Some amount of repetition on the exact same problems is necessary to lock in learning. It is often better to thoroughly understand a single example of a problem type than to work example after example understanding none of them completely.

Relevance: Good test preparation is essential to performance in physics class.

Homefun (formative/summative assessment): problems 81, 89, 91, 59 pages 193-194; problems turn in on the day stapled to the back of the test.

Summative Assessment: Unit exam objectives 1-23