A Classical Approach of Newtonian Mechanics

9 ANGULAR MOMENTUM 9.3 Angular momentum of an extended object where x^ is a unit vector pointing along the x-axis, etc. It is cl ...

9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system l 1  l 2 m m r   r O axis of rotation v 1 v 2 l Figure ...

9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system X X X fi j Fi^ mi line of centres ri Fj^ rj mj fj i Figure 8 ...

9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system × × X Consider the first expression on the right-hand side o ...

9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system axle m (^) d d m rod weight   Figure 88: Two movable weig ...

9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system bullet M v (^) b m d pivot rod Figure 89: A bullet strikes a ...

9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system  d r^ r × where I = (1/12) M (2 b)^2 = (1/3) M b^2 is the ...

9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system 5 Worked example 9.2: Angular momentum of a sphere Question: ...

9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system Now, we are told that I 1 /I 2 = 8. Hence, ω 2 = 8 × 11 = 88 ...

10 STATICS → ∞ X 10 Statics 10.1 Introduction Probably the most useful application of the laws of mechanics is the study of situ ...

10 STATICS 10.2 The principles of statics X internal forces) can be written in the form dL = τ. (10.3) dt Here, L is the total a ...

10 STATICS 10.2 The principles of statics X X × X X × × It is clear that the above principles are necessary conditions for a gen ...

10 STATICS 10.3 Equilibrium of a laminar object in a gravitational field X i=1,N .. we calculate the net torque at will—this cho ...

10 STATICS 10.3 Equilibrium of a laminar object in a gravitational field Figure 90: A laminar object pivoting about a fixed poin ...

10 STATICS 10.3 Equilibrium of a laminar object in a gravitational field Incidentally, we can use the above result to experiment ...

10 STATICS 10.4 Rods and cables 10.4 Rods and cables Consider a uniform rod of mass M and length l which is suspended horizontal ...

10 STATICS 10.4 Rods and cables T 2 A M g Figure 91: A horizontal rod suspended by two vertical cables. T = l/2 − x 1 M g. (10.1 ...

10 STATICS 10.4 Rods and cables Figure 92: A rod suspended by a fixed pivot and a cable. As usual, the centre of mass of the rod ...

10 STATICS 10.5 Ladders and walls about the pivot point to zero, we obtain l M g − T l sin θ = 0. (10.23) 2 Note that there is a ...

10 STATICS 10.5 Ladders and walls wall workman Figure 93: A ladder leaning against a vertical wall. a distance x along the ladde ...