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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