Consider the triple rotation of the x unit vector: 1 (6) 0 0 x' = R₂ (7) R₂ (7) R₂ (7)
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- Note: Make sure your calculator is in radian mode for this problem, and that you switch it back after this problem. There are two particles (1 and 2) that are moving around in space. The force that particle 2 exerts on 1 is given by: F→21(t)=Fxe−(t/T)ı^+Fysin(2πt/T)ȷ^ Where the parameters have the values: Fx=14.2 N, Fy=89 N, T=55 s.We will consider a time interval that begins at ti=0 s and ends at tf=96 s. Find the x component of the impulse from 2 on 1 between ti and tf.(a) The magnitude of the angular momentum about the origin of a particle of mass m moving with velocity v on a path that is a perpendicular distance d from the origin is given by m/v|d. Show that if r is the position of the particle then the vector J =r × mv represents the angular momentum. (b) Now consider a rigid collection of particles (or a solid body) rotating about an axis through the origin, the angular velocity of the collection being represented by w. (i) Show that the velocity of the ith particle is Vi = w X ri and that the total angular momentum J is J = Σm₁ [r}w - (r; · w)r;]. (ii) Show further that the component of J along the axis of rotation can be written as Iw, where I, the moment of inertia of the collection about the axis or rotation, is given by 1 = Σm₁p². Interpret pi geometrically. (iii) Prove that the total kinetic energy of the particles is 1².A fan blade rotates with angular velocity given by w:(t) = y – B t?. Part C If y = 5.50 rad/s and B = 0.820 rad/s³ , calculate the average angular acceleration aav-z for the time interval t = 0 to t = 2.50 s . %3D ΑΣφ Aav-z
- Engineering Dynamics need help from 4,5,6,7 thank you A ball of mass m is moving along a vertical semi-cylinder of radius R as it is guided by the arm OA. The arm moves in a clockwise direction with a constant angular velocity ω. Assume 0° ≤ Φ ≤ 90°. Neglect any friction. Neglect also the size of the ball and the thickness of the arm. Find the relationship between r, R and θ where r is the distance between O and the ball. Draw a free body diagram of the ball assuming that it is in contact with the cylinder and the arm OA. Write the equations of motion in the (r, θ) coordinate system. Find the normal force acting on the ball by the cylinder for Φ = Φ0. Find the normal force acting on the ball by the bar for Φ = Φ0. Determine the angle Φ at which the ball loses contact with the cylinder. Take m = 1 kg, R = 1.4 m, ω = 0.5 rad/s, and Φ = 60°let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 8.61 kg, with x coordinate at 3.063 m and y coordinate at 3.826 m. The second atom has a mass of 63.048 kg, with x coordinate at 87.738 m and y coordinate at 51.326 m. The third atom has a mass of 26.317 kg, with x coordinate at 42.334 m and y coordinate at 23.115 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?(14)