Chapter 10 Angular momentum
Chapter 10 Angular momentum
10-1 Angular momentum of a particle 1. Definition Consider a particle of mass m and linear momentum p at a position relative to the origin o of an inertial frame we define the angular momentum"lof the particle with respect to the origin o to be =r×P (10-1)
10-1 Angular momentum of a particle 1. Definition Consider a particle of mass m and linear momentum at a position relative to the origin o of an inertial frame we define the “angular momentum” of the particle with respect to the origin o to be (10-1) → P → r → L → → → L = r P x z y m → P → r
Its magnitude is L=rp sin 6 (10-2) where 0 is the smaller angle between r and p, we also can write it as Note that for convenience and p are in Xy plane
Its magnitude is (10-2) where is the smaller angle between and , we also can write it as Note that , for convenience and are in xy plane. L = rp sin = ⊥ = ⊥ L pr rp → P → r → P → r
2.The relation between torque and angular momentum Differentiating Eq(10-1) we obtain l dr x P+rx ∑F=x(106) Here ar dr the×P=yXP=0 d p and dt ∑ Eq(10-6) states that "the net torque acting on a particle is equal to the time rate of change of its angular momentum
2. The relation between torque and angular momentum Differentiating Eq(10-1) we obtain (10-6) Here , the → → → → → → → → = + = rF = dt d P P r dt d r dt d L → → = v dt d r = = 0 → → → → P v P dt d r and Eq(10-6) states that “the net torque acting on a particle is equal to the time rate of change of its angular momentum. → → = F dt d P
Sample pf roblem 10-1 A particle of mass m is released from rest at point p (a)Find torque and angular momentum with respect to P origin o (b show that the relation dl ∑τ yield a correct result mg:e
Sample problem 10-1 A particle of mass m is released from rest at point p (a) Find torque and angular momentum with respect to origin o (b) Show that the relation yield a correct result . b o y P x → r m mg dt d L → → =