Chapter 2: The laws of motion, Part II First two chapters: Introduce the “language of physics” Subsequent chapters: Explore objects and underlying physical concepts Homework 2.1: due Tuesday, Feb. 9 in class (Jill Bjerke) Exercises: 4, 5, 6, 7, 8, 9, 11, 12, 16, 17 Problems: 1, 3, 4, 5, 6

Announcements: Homework 1.3 due Tuesday, Feb. 2 Web page for class is: http://www.wfu.edu/~gutholdm/Physics110/phy110.htm Bring i-clicker to class You are allowed 30 missed points in the i-clicker total score (~ 160 points) Homework solutions are posted on web page (password protected) PHYSICS 110 TUTOR SESSIONS (in OLIN 101, class room) Tutor: Jillian Bjerke & Maggie Baldwin Session 1: Mo, 4-6 pm (Jill) Session 2:   We, 4-6 pm (Jill) Session 3: Th, 5-7 pm (Maggie)

Wind turbines, rotational motion Chapter 2.1 Wind turbines, rotational motion Demos and Objects Concepts Wind turbines (rotating wheel) Opening rusty screws rotating objects pirouettes levers angular displacement angular velocity angular acceleration moment of inertia (rotational mass) Torque Newton’s I. & II. law for rotational motion levers mechanical advantage

Windturbines Observations about wind turbines: (this chapter is more about rotational motion than wind turbines, generators to create electricity come later) Observations about wind turbines: Wind turbines are symmetrical and balanced A balanced wind turbine rotates smoothly An unbalanced turbine settles heavy-side down Most wind turbines have three blades Wind turbines start or stop spinning gradually Wind turbines extract energy from the wind and convert it into electrical energy

i-clicker-1 A diver does a somersault dive (spinning dive). First, she is tightly tugged in, then extends. Is the diver spinning when (right before) she hits the water? Yes, she still spins (slower). No, she will stop spinning. Not enough information.

Physics Concept Rotational Inertia In the absence of an external net torque, A body at rest tends to remain at rest. A body that’s rotating tends to continue rotating. Demonstration: Spin a Balanced Object on a Pivot Demonstration: Orient Balanced Object at Various Angles We ignore friction for the time being

Physical Quantities for rotational motion Angular Position – an object’s orientation (angle with respect to reference, i.e. horizontal Angular Velocity – its change in angular position with time Torque – a twist or spin (more later)

Angular rotation or Angular position, q SI unit of angular rotation is the radian One radian is 180°/p = 57.3° Rotation requires an axis of rotation

Angular velocity w SI unit: radians per second or just 1/sec An other unit: rotations per minute (not an SI unit). Measure of how fast an object spins Angular velocity is a vector! Use right hand rule to determine direction of vector Align right thumb with axis Align fingers with rotational movement Thumb points into direction of angular velocity vector

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.

i-clicker-2 What is the angular velocity of earth’s motion around its own axis? 1 Year 1 Day 1 revolution/year 1 revolution/day

Newton’s First Law of Rotational Motion A rigid object that’s not wobbling and that is free of outside torques rotates at a constant angular velocity. Rotational Inertia In the absence of external torques, A body at rest tends to remain at rest. A body that’s rotating tends to continue rotating.

Center of mass When an object is rotating freely (no fixed axis), it rotates about its center of mass

Center of Mass The point about which an object’s mass balances A free object rotates about its center of mass while its center of mass follows the path of a falling object Demo: Spin an object on the table and see about which point it spins.

Where is the center of mass of these objects?

We have to apply a torque to it How do we start something spinning??? We have to apply a torque to it We need a pivot point lever arm applied force Torque = force x lever arm Lever arm is perpendicular to applied force (non-perpendicular force will produce smaller torque)

Torque is a vector It has a direction and a magnitude Use the right hand rule to figure out the direction of the torque Thumb is torque, t Index finger is lever, r Middle finger is Force, F

i-clicker-4 A mechanic is trying to open a rusty screw on a ship with a big ol’ wrench. He pulls at the end of the wrench (r = 0.5 m) with a force F = 500 N at an angle of 90°. F What is the net torque the mechanics is applying to the screw? 500 Nm 0.5 m 250 Nm 250 N 90 N

Moment of inertia (rotational mass) Some objects are harder to spin than others. Moment of inertia (rotational mass) The moment of inertia or rotational mass is a measure of an object’s rotational inertia, its resistance to change in angular velocity Analogous to mass (translational inertia) Demos: rotating two sticks with different mass distribution Rotate other objects Moment of inertia depends on mass of object and mass distribution (where the mass sits with respect to axis) the axis about which the axis rotates

i-clicker: Which object is hardest to rotate??

Physical Quantities Angular Position – an object’s orientation Angular Velocity – its change in angular position with time Torque – a twist or spin Angular Acceleration – its change in angular velocity with time Moment of Inertia – measure of its rotational inertia

Torque = Moment of Inertia · Angular Acceleration Newton’s Second Law of Rotational Motion The torque exerted on an object is equal to the product of that object’s moment of inertia times its angular acceleration. The angular acceleration is in the same direction as the torque. Torque = Moment of Inertia · Angular Acceleration

Physics Concept Net Torque The sum of all torques on an object. Determines that object’s angular acceleration.

Mechanical advantage A 200 N child can support a 400 N child How does a crowbar work? How does a bottle opener work? F1 r2 r1 F2 Your bottle opener has a total length of 10 cm and the opening hook is at 1 cm. You apply a force of 10 N, what force is applied to the lid? i-clicker-5 1 N 10 N 11 N 100 N 110 N

F2 r2 F1 r1

Angular position (angle): q Summary: Angular and linear quantities Linear motion Rotational motion Position: x Angular position (angle): q Angular velocity: w Velocity: v Angular Acceleration: a Acceleration: a Torque: Force: Newton 2 Newton 2 Rotational mass: I Mass: m