PHY 210

1. PHY 210 MECHANICS II AND THERMAL PHYSICS NOOR FADHILAH BINTI MUHAMAD SAHAPINI FAKULTI SAINS GUNAAN

2. PHY 210 ASSESSMENTS • COURSE WORK 50% • TEST (2 X) 20 % • QUIZ (2 X) 10 % • LAB 20 % • LAB REPORT (6 REPORTS) 10% • SKILLS 5% • ATTITUDE AND TEAM WORK 5% • FINAL EXAMINATION 50%

3. LESSON PLAN

5. STUDENTS LEARNING TIME (SLT)How long you should spent to study PHY210 per week? Total hour you should spend per week to excel in PHY210 lecture Time for prepare lab report/lab preparation tutorial reading the notes/ strength the theories Self learning test lab Exercises/tutorial

6. CHAPTER 1 – ROTATIONAL MOTION • At the end of this chapter you should be able to: • Define and write the equation related to angular displacement, angular velocity, angular acceleration and rotational kinematics. • State the relationship between angular quantities and linear quantities • Solve the problem using rotational kinematicsequation. • Define and solve simple problems of torque and static equilibrium. • Define and understand the concepts of moments of inertia, angular momentum and its conservation. • Understand the concept and solve its simple problem regarding rotational kinetics energy, conservation of energy in translational and rotational

7. Angular Quantities – Angular displacement & Angular velocity Angular displacement: The average angular velocity is defined as the total angular displacement divided by time: The instantaneous angular velocity:

8. Angular Quantities – Angular acceleration The angular acceleration is the rate at which the angular velocity changes with time: The instantaneous acceleration:

9. Angular Quantities Angular displacement: Average angular speed: Instantaneous angular speed: Average angular acceleration: Instantaneous angular acceleration:

10. Angular velocity is a vector Right-hand rule for determining the direction of this vector. Every particle (of a rigid object): • rotates through the same angle, • has the same angular velocity, • has the same angular acceleration. q, w, a characterize rotational motion of entire object

11. Kinematic equation for angular quantities Linear motion with constant linear acceleration, a. Rotational motion with constant rotational acceleration, a.

12. Relation between angular and linear quantities Arc length s: Tangential speed of a point P: Tangential acceleration of a point P: Note: This is not the centripetal acceleration ar This is the tangential acceleration at

13. Every point on a rotating body has an angular velocity ω and a linear velocity v. They are related: If the angular velocity of a rotating object changes, it has a tangential acceleration: r r Even if the angular velocity is constant, each point on the object has a centripetal acceleration: r r r r

14. Conceptual Questions Is the lion faster than the horse? On a rotating carousel or merry-go-round, one child sits on a horse near the outer edge and another child sits on a lion halfway out from the center. (a) Which child has the greater linear velocity? (b) Which child has the greater angular velocity?

15. Example 1: Angular Quantities Angular and linear velocities and accelerations. A carousel is initially at rest. At t = 0it is given a constant angular acceleration α = 0.060 rad/s2, which increases its angular velocity for 8.0 s. At t = 8.0 s, determine the magnitude of the following quantities: (a) the angular velocity of the carousel; (b) the linear velocity of a child located 2.5 m from the center; (c) the tangential (linear) acceleration of that child; (d) the centripetal acceleration of the child; and (e) the total linear acceleration of the child.

16. Example 1: Solution r r r

17. Example 2: Kinematic equations Centrifuge acceleration. A centrifuge rotor is accelerated from rest to 20,000 rpm in 30 s. (a) What is its average angular acceleration? (b) Through how many revolutions has the centrifuge rotor turned during its acceleration period, assuming constant angular acceleration?

18. Example 2: Solution

19. Exercise 1 A wheel starts from rest and rotates with constant angular acceleration and reaches an angular speed of 12.0 rad/s in 3.00 s. 1. What is the magnitude of the angular acceleration of the wheel (in rad/s2)? A. 0 B. 1 C. 2 D. 3 E. 4 2. Through what angle does the wheel rotate in these 3 sec (in rad)? A. 18 B. 24 C. 30 D. 36 E. 48 3. Through what angle does the wheel rotate between 2 and 3 sec (in rad)? A. 5 B. 10 C. 15 D. 20 E. 25

20. Exercise 2 The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). (a) What is the angular velocity (rad/s) of the platter? (b) If the reading head of the drive is located 3.00 cm from the rotation axis, what is the linear speed of the point on the platter just below it? (c) If a single bit requires 0.50 μm of length along the direction of motion, how many bits per second can the writing head write when it is 3.00 cm from the axis?

21. Introduction of Torque • A torque is an action that causes objects to rotate. • Torque is notthe same thing as force. • For rotational motion, the torqueis what is most directly related to the motion, not the force.

22. Definition of Torque • Torque can be defined as • Tendency of force to rotate an object about the axis of rotation Unit torque = Nm • Moment of arm – distance which perpendicular from a line of force to the axis of rotation. Force (N) Moment of arm /lever arm(m) Radius of rotation Angle between radius and line of force

23. Torque • Torque is created when the line of action of a force does not pass through the center of rotation. • The line of action is an imaginary line that follows the direction of a force and passes though its point of application.

24. Torque • To get the maximum torque, the force should be applied in a direction that creates the greatest lever arm. • The lever arm is the perpendicular distance between the line of action of the force and the center of rotation θ

26. When the force and lever arm are NOT perpendicular

27. Example 3: Torque • A force of 50 newtons is applied to a wrench that is 30 centimeters long. • Calculate the torque if the force is applied perpendicular to the wrench which the lever arm is 30 cm.

28. Example 3: Solution Force is applied perpendicular to the wrench so the lever arm is 30 cm. Thus, torque is

29. Example 4: Calculate net torque Two thin disk-shaped wheels, of radii RA = 30 cm and RB = 50 cm, are attached to each other on an axle that passes through the center of each, as shown. Calculate the net torque on this compound wheel due to the two forces shown, each of magnitude 50 N.

30. Example 4: Solution The torque due to FA tends to accelerate the wheel counterclockwise, whereas the torque due to FB tends to accelerate the wheel clockwise.

31. Exercise 3 • It takes 50 Nto loosen the bolt when the force is applied perpendicular to the wrench. • How much force would it take if the force was applied at a 30-degree angle from perpendicular? (ans:57.74 N) • A 20-centimeter wrench is used to loosen a bolt. • The force is applied 0.20 m from the bolt.

32. Static Equilibrium • When an object is in static equilibrium, • the net force applied to it is zero, • the net torque applied to it is zero, • Examples • Book on table • Hanging sign • Ceiling fan – off • Ceiling fan – on • Ladder leaning against wall Equilibrium implies the object is at rest (static) or its center of mass moves with a constant velocity (dynamic) We will consider only with the case in which linear and angular velocities are equal to zero, called “static equilibrium”: vCM= 0 and w = 0

33. Conditions for Equilibrium • The first condition of equilibrium is a statement of translational equilibrium • The net external force on the object must equal zero • It states that the translational acceleration of the object’s center of mass must be zero

34. Conditions for Equilibrium • If the object is modeled as a particle, then this is the only condition that must be satisfied • For an extended object to be in equilibrium, a second condition must be satisfied • This second condition involves the rotational motion of the extended object

35. Conditions for Equilibrium • The second condition of equilibrium is a statement of rotational equilibrium • The net external torque on the object must equal zero • It states the angular acceleration of the object to be zero • This must be true for any axis of rotation

36. Conditions for Equilibrium of a rigid object • The net force equals zero • If the object is modeled as a particle, then this is the only condition that must be satisfied • The net torque equals zero • This is needed if the object cannot be modeled as a particle • These conditions describe the rigid objects in the equilibrium analysis model.

37. Example 5: Static equilibrium • When an object is in static equilibrium, the net torque and net force applied to it is zero. • Rotational equilibrium is often used to determine unknown forces. • What are the forces (FA, FB) holding the bridge up at either end?

38. Example 5: Solution

39. Exercise 4 • A boy and his cat sit on a seesaw. • The cat has a mass of 4 kg and sits 2 m from the center of rotation. • If the boy has a mass of 50 kg, where should he sit so that the see-saw will balance?

40. Rotational Inertia Key Question: Does mass resist rotation the way it resists acceleration?

41. Rotational Inertia • Inertia is the name for an object’s resistance to a change in its motion (or lack of motion). • Rotational inertia is the term used to describe an object’s resistance to a change in its rotational motion. • An object’s rotational inertia depends not only on the total mass, but also on the way mass is distributed.

42. Rotational Inertia • To put the equation into rotational motion variables, the force is replaced by the torque about the center of rotation. • The linear acceleration is replaced by the angular acceleration.

43. Rotational Inertia • A rotating mass on a rod can be described with variables from linear or rotational motion.

44. Rotational Inertia • The product of mass × radius squared (mr2) is the rotational inertia for a point mass where r is measured from the axis of rotation.

45. Moment of Inertia • The sum of mr2 for all the particles of mass in a solid is called the moment of inertia (I). • Moment of inertia (rotational inertia) of an object depends on: • the axis about which the object is rotated. • the mass of the object. • the distance between the mass(es) and the axis of rotation.

46. Moment of Inertia The moment of inertia of some simple shapes rotated around axes that pass through their centers.

47. Moment of inertia for some objects

48. Rotation and Newton's 2nd Law If you apply a torque to a wheel, it will spin in the direction of the torque. The greater the torque, the greater the angular acceleration.

49. Rotational Kinetic Energy A rotating object (collection of i points with mass mi) has a rotational kinetic energy of Where: Moment of inertia or rotational inertia

50. Conservation of energy (including rotational energy): Again: If there are no non-conservative forces energy is conserved. Rotational kinetic energy must be included in energy considerations!