A Classical Approach of Newtonian Mechanics

10 STATICS 10.6 Jointed rods → thermore, the torques associated with these two forces act in opposite directions. Hence, setting ...

10 STATICS 10.6 Jointed rods Y 2 Figure 94: Three identical jointed rods. reactions on one another, in accordance with Newton’s ...

10 STATICS 10.6 Jointed rods Y 2 = 0, (10.43)^ X 1 = X 2 = X 3 = X, (10.44)^ Y 1 = Y 3 = −M g. (^) (10.45) There now remains onl ...

10 STATICS 10.6 Jointed rods ! l 1 l 2 coordinate system correspond to the pivot point. The centre of mass of the first rod is s ...

10 STATICS 10.6 Jointed rods Worked example 10.2: Rod supported by a cable Question: A uniform rod of mass m = 15 kg and length ...

10 STATICS 10.6 Jointed rods Worked example 10.3: Leaning ladder Question: A uniform ladder of mass m = 40 kg and length l = 10 ...

10 STATICS 10.6 Jointed rods R truck S l/3 l which yields (m g/2 + M g x/l) S = tan θ = (0.5 × 40 × 9.81 + 80 × 9.81 × 7/10) tan ...

10 STATICS 10.6 Jointed rods Here, we have made use of the fact that centre of mass of the bridge lies at its mid-point. It foll ...

10 STATICS 10.6 Jointed rods N Setting the net horizontal force on the rod to zero gives Y 1 + Y 3 = 0. Setting the net vertical ...

11 OSCILLATORY MOTION ∝ 11 Oscillatory motion 11.1 Introduction We have seen previously (for instance, in Sect. 10.3) that when ...

11 OSCILLATORY MOTION 11.2 Simple harmonic motion m system is representative of the motion of a wide range of systems when they ...

11 OSCILLATORY MOTION 11.2 Simple harmonic motion ω t − φ 0 ◦^90 ◦ 180 ◦ 270 ◦ x +a 0 −ω^2 a 0 −ω a 0 −a 0 +ω^2 a 0 +ω a 0 x ̇ x ...

11 OSCILLATORY MOTION 11.2 Simple harmonic motion 0 ! executes simple harmonic motion about its equilibrium state. In physical t ...

11 OSCILLATORY MOTION 11.3 The torsion pendulum ±   torsion wire disk fixed support Figure 96: A torsion pendulum. since m ω^ ...

11 OSCILLATORY MOTION 11.4 The simple pendulum I to restore the wire to its untwisted state. For relatively small angles of twis ...

11 OSCILLATORY MOTION 11.4 The simple pendulum fixed support pivot m g Figure 97: A simple pendulum. Fig. 97. This setup is know ...

11 OSCILLATORY MOTION 11.4 The simple pendulum s ' Thus, we can write τ = −m g l sin θ. (11.22) Combining the previous two equat ...

11 OSCILLATORY MOTION 11.5 The compound pendulum Pivot point Centre of mass Figure 98: A compound pendulum. 11.5 The compound pe ...

11 OSCILLATORY MOTION 11.6 Uniform circular motion ' I s Note that the reaction, R, at the peg does not contribute to the torque ...

11 OSCILLATORY MOTION 11.6 Uniform circular motion y x Figure 99: Uniform circular motion. Since the object is executing uniform ...