Angular Kinematics Ch 9 Notes. What is a radian? 1 Θ rad = 57.3 ͦ of twist.

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Angular Kinematics Angular Kinematics Ch 9 Notes Ch 9 Notes

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Transcript of Angular Kinematics Ch 9 Notes. What is a radian? 1 Θ rad = 57.3 ͦ of twist.

  • Angular KinematicsCh 9 Notes

  • What is a radian?1 rad = 57.3 of twist

  • Angular Variables = S / r1 = 57.3 of twist in a seconds time = rad / 1 s1 = change in angular speed equal to 57.3 of twist per second = / 1 s Srad

  • Angular Kinematics DefinitionsAngular Velocity: amount of twist per time = / tunits: rad/s

    Angular Acceleration: amount of change in twist per time = / tUnits: rad/s2

  • Linking Linear with Angular

    vt = x/t = C/T = 2r/T1 rev = 2 radians = 6.28 radians

    = S / r = vT / r = aT / r

    S

  • Centripetal and Radial AccelCentripetal or radial accelerationac = ar = v2/r in linear units ac = ar = r2 in angular units

  • Clockwise (CW) vs. Counterclockwise (CCW)CCW is +, CW is throughout course

  • 2. Finding radial acceleration-angular unitsWhat is the radial acceleration of a motorcycle proceeding in a circular cage of diameter 14.0 m if it is moving at an angular velocity of 2.0 rad/s?

    28 rads/s2

  • 1. Finding radial acceleration-linear unitsWhat is the radial acceleration of an object that spins with a linear speed of 4.00 m/s at a 0.80 m distance from the axis of rotation?

    20 m/s2 or 20 rads/s2

  • A closer look at acceleration// to motion: tangential accelerationLeads to more/less rpmPerp. to motion: radial acceleration or centripetal accelerationGives inward acceleration needed to make circular motionAcceleration can be broken down

  • Galileos Formulas Work for Rotation!!!!Angular displacement: (# radians spun) radAngular velocity: (radians spun per second)rad/sAngular acceleration: ( in rps per sec) rad/s2

    Vf = vi + atf = + t

    Vf2 = Vi2 + 2ax f2 = i2 + 2

    x = vit + at2 = it + 1/2t2

  • Rotation and Graphing for x for v for aSLOPES TO GO UPAREAS UNDER CURVE TO GO DOWN

  • 3. What is angular acceleration?An piece of tape at the edge of the disk of radius 0.19 m slows from a speed of 2.00 m/s to a speed of 1.00 m/s in a 6.00 second time frame. What is the angular acceleration of the tape? What is the angular acceleration of the inside edge of the disk (r = 0.03 m)?

  • 4. What is the final angular velocity?An object being swung around with a radius of 0.50 m is subject to an angular acceleration of 0.25 rad/s2 for a 3.00 second time frame. If it started with a speed of 8.00 m/s, what is its angular velocity after the three seconds have elapsed?What number of rotations will have occurred in this 3.0 sec time span?

  • 5. What is the angular acceleration?A disk is spun for a total of 62 rotations. It begins at an angular velocity of 1.8 rad/s and due to friction this value drops to 1.2 rad/s by the 62nd rotation. What is this disks angular acceleration?

  • Moment of InertiaInertia of SpinMeasure of the unwillingness of a material to want to rotateIncreases with greater overall mass, no matter what the shape of the materialShape affects momentIf all mass on outside of orbit, I = mr2Others p. 298

  • What has more kinetic energy, a knuckleball pitched at 70 mph, or a changeup pitched at 70 mph?Close but not identical!!!!!!

  • Rotational Kinetic EnergyEnergy of Spin as opposed to Energy of MotionKErot = I 2

    Objects that are rolling tend to have both forms of KE!

  • Example: Total KEWhat is the total KE of a basketball (0.60 kg, diameter 30.0 cm) that is rolling at a speed of 2.00 m/s on the ground?

  • Moment of InertiaMoment of inertia generally higher the more mass is distributed further from the axis of rotation

  • Moment of inertia changes for the same material according to what spin axis you choose for it.

  • Shapes & Moments of Inertia

  • The disk cylinder has a lower moment due fact that mass closer to axis of rotation is easier to rotate = F lT = I

  • Extras: Ch 10-11Angular Momentum: tendency for a system to rotateL = I L = r m vunits are kg m2/sAngular Momentum for a system is conservedFigure skatersElliptical orbitsBike tire

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