Consider the spherical pendulum, which consists of a mass m suspended by a string from the ceiling. The mass is free to swing in both directions but maintains a constant distance from the point of suspension. Choose spherical polar coordinate θ, ϕ as generalized coordinates for this problem. What is T(θ, ˙θ, ϕ, ϕ˙)?

Q: A high-speed aircraft takes-off in the xyz-plane and the coordinates are given by x(t) = αt, y(t) =…

A:

Q: Given the curve C parametrized by the vector equation r (t)=3sin(t)i+[2−sin(t)+cos(t)]j−3cos(t)k,…

A: The vector equation is : r (t)=3sin(t)i^+[2−sin(t)+cos(t)]j^−3cos(t)k^, t∈[0;2π]   The tangent…

Q: At the instant of the figure, a 1.3 kg particle P has a position vector 7 of magnitude 1.4 m and…

A: Angular momentum, L = m(r × v) L = mrv sin (180 - θ2) k L = mrv sin(180 - 30) k L =…

Q: A point is located in a polar coordinate system by the coordinates r = 7.3 m and 8 = 23°. Find the…

A:

Q: How do I do part B?

A:

Q: A pendulum is connected to a rope 3 m long, which is connected to a ceiling 4 m high. The angle…

A:

Q: Newton’s Second Law of Motion in vector form states thatF = dp/dt , where F is the force acting on…

A: Newton’s Second Law of Motion in vector form states that : F=dPdt  ....(1) where F is the force…

Q: Write the given vectors in terms of its components and the corresponding unit vector and then verify…

A:

Q: motion of the point K moving along the plane is given by the equation x = 3sin (t), y = 2cos (t).…

A: GIVEN x= 3 sint y=2 sint

Q: You are looking down on a disc that is spinning counterclockwise in the xy plane (positive z points…

A:

Q: (x^2) + (y^2) + (z^2) = 1 and (x^2) + (y^2) + (z^2) = 4

A:

Q: Consider the vectors a = i + 8j + 4k and b = 7i − 6j − 6k, where i, j, and k are…

A:

Q: Given a vector (77, 48, 22) and another vector (4, 49, 67) what is the z-component of their sum?

A: Given that Vector 1 (A)= (77, 48, 22)  And , vector 2 (B)= (4, 49, 67) Let i, j and k be the unit…

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A:

Q: On a plane flat surface with "up" given as +y and "right" given as +x, we add two vectors. One of…

A:

Q: Let vectors A⃗=(2,−4) A → = ( 2 , − 4 ) and B⃗=(−3,1) B → = ( − 3 , 1 ) . Calculate the following:…

A:

Q: Let z = z(t) and y = y(t) (where tis the variable of time) be the horizontal and vertical positions…

A: Given: Position in XY plane as X=xtY=yt At point α,β, where  α<0β>0     means particle is in…

Q: A spool of mass m and radius R rests on a horizontal surface. Its momentum of inertia relative to…

A:

Q: A student club is designing a trebuchet for launching a pumpkin into projectile motion. Based on an…

A: The problem is asking for the derivative of the vertical position of the pumpkin trajectory with…

Q: Let a = (5,-1, 2) and 6 = (3, 2, -2). b Find the angle between the vector (in radians)

A:

Q: Consider the vectors a = i + 8j + 4k and b = 7i − 6j − 6k, where i, j, and k are…

A:

Q: You are looking down on a disc that is spinning counterclockwise in the xy plane (positive z points…

A:

Q: Consider the vectors a = i + 8j + 4k and b = 7i − 6j − 6k, where i, j, and k are…

A: The vector, a→=i^+8j^+4k^ The vector, b→=7i^-6j^-6k^ where i^, j^, k^ are unit vectors in the…

Q: Two twin sisters, Ana and Bia, compare their ages in different travel situations between SP and a…

A: Given: distance between the cities=L

Q: A→ times B→ = What is the angle between A and B? What is 2B times 3C?

A: Expanding this determinant:A×B =i[(1)(1)−(0)(−4)]−j[(2)(1)−(−4)(−3)]+k[(2)(0)−(1)(−3)]…

Q: Can you help me with 7.54 b?

A: P 7.54 (b):According to the law of conservation of energy,Substitute the values, to find the maximum…

Q: On the surface of the earth, the gravitational field (with z as vertical coordinate measured in…

A: (A). The potential function for given F is  fx,y,z=-gz

Q: magnitude of A

A:

Q: Note: Make sure your calculator is in radian mode for this problem, and that you switch it back…

A: In this question we have to find the parameters having the said asked values for the particles…

Q: Consider a solid sphere, determined by the volume x^2 + y^2 + z^2 ≤ R^2 , with a non uniform density…

A:

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A: Let F1, F2, and F­3 denote the three forces, θ1, θ2, and θ3 denote the three angles of the forces…

Q: Consider the vectors: A = 2î + 5j. B = 5i + 4j, and C = A - B. What is the direction of C , measured…

A: Here we have to subtract B from A component wise. C vector is coming out to be in 2nd quadrant. So…

Q: A star of mass M = 1.81 x 10kg is the origin of a coordinate system. A comet of mass m = 7.87 x 10¹2…

A: Given a star of mass  M=1.81×1030 kg is at the origin of a coordinate system. hence the coordinates…

Q: Consider the 3D vectors C and D defined as C = 4i + 5j - 12k and D = 12i - 8j + 2k. Which of the…

A: Given,  C = 4i + 5j - 12k   And  D = 12i - 8j + 2k

Q: Consider a tower 50 m south from your home, where the coordinate frame is centred at your home, such…

A: For the given condition the coordinates of the foot of the tower are given as (0, - 50, 0)  and the…

Q: a certain corner of a room is selected as the origin of a retangualr coordinate system. A fly is…

A: Write the given values with suitable variables. x=3.7y=1.3

Q: A particular point P on a rigid object has co-ordinates (x, y, z) = (2.0,2.0,0). The object is now…

A:

Q: A thin rod of mass M and length is suspended vertically from a frictionless pivot at its upper end.…

A:

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A: Given: The resultant magnitude R and the angle θ between the x-axis and the line of action of the…

Q: The two vectors a→ and b→ in the figure have equal magnitudes of 10.2 m and the angles are θ1 = 30°…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…