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AP Physics Chapter 11-12 Key Equations and Ideas Kinematic Equations Rotation (constant ang accel) s = r d dt d dt v = r a = r KR = ½I2 f = i + it + ½t2 f2 = i2 + 2(f – i) f = i + t f = i + ½(f + i)t n ac = 2r I m r i 1 dm = dV 2 i i 2 dV = 4r dr (spherical) (discrete) I r 2 dm (distributed) I = Icom + Mh2 (parallel axis theorem) Torque Rotational Work and K = r x F = rF sin = rF rF = I W = K = ½If2 - ½Ii2 Angular Momentum dL L = I net L r̂ x p̂ dt dL When net = 0, 0 dt Lf = Li (always) Iff = Iii W= f i d W = (f - i) (constant ) d ( ) dW dt dt g Yo-Yo: acom I 1 com2 MR P CW = CCW Key Ideas: An angular displacement in the counterclockwise direction is positive and one in the clockwise direction is negative. To find the extreme value (e.g. minimum or maximum) of a function, take the derivative and set it equal to zero. All the linear quantities and equations have corresponding angular quantities and equations. Remember the linear equations and you can immediately write the angular equations by substituting in the corresponding angular quantities. Always remember to use radians, not degrees in the equations above. In rotational motion, there can be tangential acceleration (i.e. in the direction of the velocity vector) and radial acceleration (i.e. pointing towards the center of rotation). A body will freely rotate about an axis that always passes through the center of mass of the body. If a body is forced to rotate about an axis that does not pass through the center of mass, use the Parallel Axis Theorem to calculate its rotational inertia. A body with translational motion has linear kinetic energy. A body that only rotates has rotational kinetic energy. A rolling body has both linear and rotational kinetic energy. The sum of all the torques acting on a particle or on a system of particles is equal to the time rate of change of the angular momentum of that particle or the system or particles, respectively. If the net external torque acting a system is zero, the angular momentum of the system remains constant, no matter what changes take place within the system. If the component of the next external torque on a system along a certain axis is zero, then the component of the angular momentum of the system along that axis cannot change, no matter what changes take place within the system. Conservation of angular momentum always holds in a closed (i.e. no matter passes in or out) and isolated (i.e. no external forces) system. Angular momentum is conserved in each dimension!!