AP Physics Chapter 10 Summary Section 10.2: Rotational Variables
θ (theta) – angular displacement – radians ω (omega) – angular velocity – radians/sec α (alpha) = angular acceleration – radians/sec 2 t – still time and still in seconds Measuring Angular Displacement - θ = L/r 360° = 2π radians = 1 revolution v= ωr :Linear velocity = angular velocity x radius a = αr: Linear acceleration = angular acceleration x radius
Sections 10.3 – 10.5 Linear
V = v 0 +at x = v V 2 0 = v t+½at 0 2 2 +2ax Angular ω=ω 0 +άt θ=ω 0 t+½άt 2 ω 2 =ω 0 2 +2άθ V avg = (v 0 +v f )/2 ω avg =(ω 0 +ω f )/2
Section 10.6: Kinetic Energy of Rotation
The rotational inertia of an object depends upon its shape and its mass. Values of I are always some form of the equation I=_mr 2 where the blank represents some fraction. Torque = Iα = rotational inertia x angular acceleration. Hence Fr = Iα. The Kinetic Energy of a rotating body is given by K = ½Iω 2 .
Section 10.7: Calculating Rotational Inertia
I = ∫ r2 dm For various objects the results of these calculations can be found on page 253 in table 10.2
Parallel axis Theorem
If you know the I value for a body through the center of mass then a shortcut to finding its I value for a parallel axis is given as: I = I cm + Mh 2 Where h is the perpendicular distance between the axes.
Section 10.8: Torque
Torque = Fr = force x radius. Torque is measured in newton•meters which means that it has the same units as work in a linear system.
Section 10.9: Newton’s Second Law for Rotation
Like force in a linear system, torque can be summed in order to solve problems. ∑τ = clockwise τ - counterclockwise τ = Fr = Iα
Section 10.10: Work and Rotational Kinetic Energy
x v = dx/dt
Rotation about a fixed axis
Angular Displacement Angular Velocity Angular Acceleration Rotational Inertia Θ Acceleration a =dv/dt Mass (translational inertia) m Force Work Kinetic Energy Power Linear Momentum F = ma W = ∫F dx K = ½ mv 2 P = W/t = Fv ρ=mv Torque Work Kinetic Energy Power Angular Momentum ω=dθ/dt α=dθ/dt I τ=Iα W = ∫τ dθ K= ½ Iω P = τω L = Iω 2