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- A 0.2-kg particle P is constrained to move along the vertical-plane circular slot of radius r = 1.4 m and is confined to the slot of arm OA, which rotates about a horizontal axis through O with a constant angular rate 2 = 2.0 rad/s. For the instant when 3 = 17°, determine the magnitue of the force N exerted on the particle by the circular constraint and the magnitude of the force R exerted on it by the slotted arm. Answers: N = R= i -0.688 i 1.2079 B N NFind the centroid (?̅ and ?̅) Compute moments of intertia about x-axisà ở từ if a = 2.8i+ 5.7 j – 8.1k, = b = − 4.9î + 4.4ĵ + 3.8k, and What are (a) the x component, (b) the y component, and (c) the z component of 7 1.8î + 2.8ĵ + 4.6k . (d) Calculate the angle between and the positive z axis. (e) What is the component of a along the direction of b? (f) What is the magnitude of the component of a perpendicular to the direction of b but in the plane of a and b? =
- (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.Find the answer for the given: Let L be the length. Let M be the mass. A rod that has L and M was hunged from the one end of a frictionless pivot, and it was hanged vertically at rest (intially) A person fired one small ball of clay with mass (m) to the rod with a speed V(initial) and stuck to the end of the non pivoted area. Find the angle Of greatest rotation for the rod/clay system? M M,L V(initial)A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.5 meters, and a mass M = 251 kg. A small boy of mass m = 41 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on.Randomized VariablesR = 1.5 metersM = 251 kgm = 41 kgv = 1.8 m/s (a) Calculate the moment of inertia of the merry-go-round, in kg ⋅ m2. Part (b) Immediately before the boy jumps on the merry go round, calculate his angular speed (in radians/second) about the central axis of the merry-go-round.(c) Immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry-go-round and boy.(d) The boy then crawls towards the center of the merry-go-round along a radius. What is the angular speed in radians/second of the merry-go-round when the boy is half way between the edge and the center of the merry go round?(e) The…
- Current Attempt in Progress Three dimensions. Three point particles are fixed in place in an xyz coordinate system. Particle A, at the origin, has mass ma. Particle B, at xyz coordinates (2.00d, 2.00d, 2.00d), has mass 4.00ma, and particle C, at coordinates (-3.00d, 2.00d, -3.00d), has mass 4.00mA. A fourth particle D, with mass 3.00ma, is to be placed near the other particles. If distance d = 4.20 m, at what (a) x, (b) y, and (c) z coordinate should D be placed so that the net gravitational force on A from B, C, and D is zero? %3D (a) Number i Units (b) Number Units (c) Number Units > >I need help with this physics question.