Torsion Pendulum Sinceτ=-k0,τ= la becomes 0 T (L d20 -o0 where at Similar to"mass on spring, except I has taken the place of m(no surprise) Physics 121: Lecture 22, Pg 11
Physics 121: Lecture 22, Pg 11 Torsion Pendulum... Since = -k = Ia becomes I wire Similar to “mass on spring”, except I has taken the place of m (no surprise) d dt 2 2 2 = − = k I where
Lecture 22: Act 3 Period All of the following pendulum bobs have the same mass Which pendulum rotates the fastest i.e. has the smallest period?(The wires are identical) R R R A) B) c) D) Physics 121: Lecture 22, Pg 12
Physics 121: Lecture 22, Pg 12 Lecture 22: Act 3 Period All of the following pendulum bobs have the same mass. Which pendulum rotates the fastest, i.e. has the smallest period? (The wires are identical) R R R R A) B) C) D)
SHM So Far The most general solution is X= Acos(ot + o) where a amplitude o= frequency φ= phase For a mass on a spring For a general pendulum MaR For a torsion pendulum Physics 121: Lecture 22, Pg 13
Physics 121: Lecture 22, Pg 13 SHM So Far The most general solution is x = Acos(t + ) where A = amplitude = frequency = phase For a mass on a spring For a general pendulum For a torsion pendulum = k m = MgR I = k I
Velocity and Acceleration Equations for x, v, and a Position: x(t) =Acos(ot +o) Velocity v(t)=-oAsin(ot +o) Starting with Acceleration: a(t)=-02Acos(ot +o) angeφpant t=0 A MAX A aMAx=02A k ∧m 0 Physics 121: Lecture 22, Pg 14
Physics 121: Lecture 22, Pg 14 Velocity and Acceleration k x m 0 Position: x(t) = Acos(t + ) Velocity: v(t) = -Asin(t + ) Acceleration: a(t) = -2Acos(t + ) Starting with angle ant t=0 xMAX = A vMAX = A aMAX = 2A Equations for x, v, and a