Transcript Physics_U8
Unit 8: Circular Motion Section A: Angular Units Corresponding Textbook Sections: – 10.1 PA Assessment Anchors: – S11.C.3.1 Angular Position Defined as the angle, , that a line from the axle to a spot on the wheel makes with a reference line Unit: Radian (rad) [dimensionless] Sign convention for angular position: If > 0, counterclockwise rotation If < 0, clockwise rotation Converting between degrees and radians 1 revolution = 360 = 2 rad 1 rad = 57.3 Convert the same way you would between any other units. Section B: Angular / Linear Relationships Corresponding Textbook Sections: – 10.3 PA Assessment Anchors: – S11.C.3.1 Arc Length The arc length is the distance from a reference line to a spot of interest on a circle. Equation: s = r Angular Velocity Symbol: av t Units: s-1 or 1/s Sign Convention for If > 0 Counterclockwise rotation If < 0 Clockwise rotation Practice Problem #1 An old phonograph rotates clockwise at 33⅓ rpm. What is the angular velocity in rad/s? Practice Problem #2 If a CD rotates at 22 rad/s, what is its angular speed in rpm? Period The period is the time it takes to complete one revolution. Units: seconds (s) T 2 Practice Problem #3 Find the period of a record that is rotating at 45 rpm. Angular Acceleration The change in angular speed of a rotating object per unit of time. Units: rad/s2 t Practice Problem #4 As the wind dies, a windmill that was rotating at 2.1 rad/s begins to slow down with a constant angular acceleration of 0.45 rad/s2. How long does it take for the windmill to come to a complete stop? Section C: Angular Kinematics Corresponding Textbook Sections: – 10.2 PA Assessment Anchors: – S11.C.3.1 Relationship between angular and linear quantities Linear Quantity Angular Quantity x v ω a α Based on these relationships, we can rewrite the kinematics equations from 1-D and 2-D Kinematics Angular Kinematics Equations v v o at = o t 1 2 x x o v o t at 2 1 2 = o o t t 2 v v 2ax 2 2 2 o 2 2 o So, basically… These are just variations of equations we already know how to use. They work the same way as the linear equations. We’ll use the same setup as before: • Data table, equation, picture, etc… Practice Problem #1 To throw a curveball, a pitcher gives the ball an initial angular speed of 36 rad/s. When the catcher gloves the ball 0.595 s later, its angular speed has decreased to 34.2 rad/s. What is the ball’s angular acceleration? Practice Problem #2 Based on the last problem, how many revolutions does the ball make before being caught? Practice Problem #2 Refer to Example 10-2 on page 280 Section D: Torque Corresponding Textbook Sections: – 11.1, 11.2 PA Assessment Anchors: – S11.C.3.1 What is Torque? Torque is the rotational equivalent of force It depends on: – Force applied – Distance from the force to the axis of rotation More on Torque… Equation: rF Greek Letter “tau” Units: Nm Axis of Rotation (where it turns) Practice Problem #1 If the minimum required torque to open a door is 3.1 Nm, what force must be applied if: – r = 0.94 m – r = 0.35 m Section E: Moment of Inertia Corresponding Textbook Sections: – 10.5 PA Assessment Anchors: – S11.C.3.1 What is “Moment of Inertia”? The “rotational mass” of an object – Rotational mass depends on actual mass, radius, and distribution of mass Useful for determining rotational KE: 1 2 KE I 2 Moment of inertia Practice Problem #1 What is the moment of inertia of a hollow sphere with mass of 40 kg and radius of 3 m? Practice Problem #2 A grindstone with radius of 0.61 m is being used to sharpen an axe. If the linear speed of the stone relative to the ax is 1.5 m/s, and the stones rotational KE is 13 J, what is its moment of inertia?