A Classical Approach of Newtonian Mechanics

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions m (^1) v i1 i m 1 + m 2 vf f (^) x vi2 m 2 y Figure 56: A totally ...

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions M m L v two equations [i.e., Eqs. (6.64) and (6.65)] and two unknown ...

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions Suppose that, after the cannonball strikes the far wall of the carri ...

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions 3 p p  By definition, the net momentum change is equal to the impu ...

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions i (^2) After the skater catches the ball, the combined momentum of t ...

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions 2 × f The final kinetic energy of the system is K = 1 (M + m) v^2 = ...

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions m 2 m 1 vi1 m 2   m 1 vf1 which has the non-trivial solution y = ...

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions i 2 i1^ f 2 f1^2 f2^ The^ above^ pair^ of^ equations^ can^ be^ combi ...

7 CIRCULAR MOTION 7 Circular motion 7.1 Introduction Up to now, we have basically only considered rectilinear motion: i.e., moti ...

7 CIRCULAR MOTION 7.2 Uniform circular motion proportional to the angle θ: but, what is the constant of proportionality? Well, a ...

7 CIRCULAR MOTION 7.3 Centripetal acceleration seconds. Here, T is the repetition period of the circular motion. If the object e ...

7 CIRCULAR MOTION 7.3 Centripetal acceleration → ' Y Q v^ Z v v X P v^ r    Figure 58: Centripetal acceleration. simply δθ ...

7 CIRCULAR MOTION 7.3 Centripetal acceleration cable T r m weight v m Figure 59: Weight on the end of a cable. Suppose that a we ...

7 CIRCULAR MOTION 7.4 The conical pendulum m g Figure 60: A conical pendulum. 7.4 The conical pendulum Suppose that an object, m ...

7 CIRCULAR MOTION 7.5 Non-uniform circular motion s s = ., = acts towards the centre of the circle. In other words, T sin θ = m ...

7 CIRCULAR MOTION 7.5 Non-uniform circular motion er Figure 61: Polar coordinates. and θ. Here, r is the radial distance of the ...

7 CIRCULAR MOTION 7.5 Non-uniform circular motion whereas the acceleration is written a = v ̇ = ar er + aθ eθ. (7.28) Here, vr i ...

7 CIRCULAR MOTION 7.5 Non-uniform circular motion .i e. = q sin θ + cos^2 θ = 1. (7.35) r .e i θ. = q cos^2 θ + sin^2 θ = 1. (7. ...

7 CIRCULAR MOTION 7.5 Non-uniform circular motion i ei^   e  ei^  er sin   cos  Re(z) Figure 63: Representation ...

7 CIRCULAR MOTION 7.5 Non-uniform circular motion Comparing with Eq. (7.28), recalling that e i θ represents er and i e i θ repr ...