Introduction to Statics and Dynamics by Pratap R., Ruina A.

By Pratap R., Ruina A.

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By Pratap R., Ruina A.

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4) F θ O r |F | sin θ ∼ O θ |r | If you curl the fingers of your right hand in the direction of rotation caused by a force your thumb points in the direction of the moment vector. θ ∼ The expression we have found for the right side of eqn. 4 is the 2D cross product of vectors r and F . We can now apply the concept to any pair of vectors whether or not they represent force and position. The 2D cross product is defined as : de f = ˆ |A| |B| sin θ k. 22: The moment of a force is either the product of its radius with its perpendicular component or of its lever arm and the full force.

In the x y plane, the 2D moment is a vector in the kˆ direction (straight out of the plane). So eqn. 3 becomes ˆ M/C = | r | |F | sin θ k. 4) F θ O r |F | sin θ ∼ O θ |r | If you curl the fingers of your right hand in the direction of rotation caused by a force your thumb points in the direction of the moment vector. θ ∼ The expression we have found for the right side of eqn. 4 is the 2D cross product of vectors r and F . We can now apply the concept to any pair of vectors whether or not they represent force and position.

7k. F = ˆ and the x, y, and z axes be θ, φ and ψ respectively. 4. 4o . 6o . 6o 32 CHAPTER 2. 14 Projection of a vector in the direction of another vector: Find the component of F = 5 Nˆı + 3 Nˆ + 2 Nkˆ along the vector r = 3 mˆı − 4 mˆ. ˆ gives the projection of Solution The dot product of a vector a with a unit vector λ ˆ Therefore, to find the component of the vector a in the direction of the unit vector λ. ˆ r along r and dot it with F . 4 N. 4 m/s2 ıˆ +a3 ˆ. Separate the scalar equations in the ıˆ, ˆ, and kˆ directions.

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