If the rigid body rotates 30deg about the global X-axis and the origin of the body translates to (X, Y, Z)=(500, 0 600), the final point in the Global frame is (500 -100, 773.2). Find the origin position (x1, y1, z1) in the body coordinate frame by using the inverse 4X4 matrix.

Q: Find a vector of magnitude 8 in the direction of i = (-4, –6, –1). Vector is Find a vector of…

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Q: A geocentric satellite has orbital elementsi = 28.5 , Ω = 152 , and ω = 180 . Determine its position…

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Q: A planet of mass 5 x 1024 kg is at location (4 x 1011, -4 x 1011, o) m. A star of mass 5 x 1030 kg…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: A planet of mass 5 ⨯ 1024 kg is at location m. A star of mass 4 ⨯ 1030 kg is at location m. It will…

A: The position of the planet and star is drawn below:

Q: find its magnitude and direction (r,θ)

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A: Initial velocity in horizontal direction   ux = voAcceleration in horizontal direction    ax = 0

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A: We have givena=912=9.5 "b=11"θ=43°γ=21°

Q: Suppose that q1 = 3 µC (3.0×106 on the figure in cm. Find the angle in degrees that the net force on…

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Q: A point P =( 1,7,1 ) is attached to a rotating frame, the frame rotates 76 degree about the OX axis…

A: Ans: Point P is rotated 76° about the OX axis of the reference frame.  Then suppose new coordinates…

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A: The centre of semicircle is at the origin of our coordinate system…

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Q: The merry-go-round rotates at a constant angular velocity of w = 3,1 rad/s. Assume that an observer…

A: Constant Angular velocity (w) = 3.1 rad/s Radius (r) = 3.6 m

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Q: A force vector has magnitude F makes an angle of 69° with respect to the x-axis of a Cartesian space…

A: Given, a force vector has magnitude F makes an angle of x=69° with respect to the x-axis of a…

Q: Planet 1 has mass 3M and radius R, while Planet 2 has mass 4M and radius 2R. They are separated by…

A: Given data: Mass of the planet 1, m1=3M The radius of planet 1,r2=R Mass of the planet 2, m2=4M The…

Q: Relative to a nonrotating Cartesian coordinate frame with the origin at the center O of the earth, a…

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Q: Stars and black holes in a binary system orbit each other in circular orbits of radius r1 and r2…

A: mass of an orbital m= 1.98x1030 kg v1 =5.36 times faster than our Sun T=30 hours r1=?,r2=?m2=?

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A: Magnitude of B is 4.80 m Angle of B is θB=60∘ Difference of angle of C and A is θC-A=25∘ Magnitude…

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A: To determine the magnitude of vector A in the "rho" direction in cylindrical coordinate system at P,…

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A: Given, mass as, m1=Mm2 =m radius=R, distance=r.

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Q: A planet of mass 5 ⨯ 1024 kg is at location <4 ⨯ 1011, −4 ⨯ 1011, 0> m.  A star of mass 4 ⨯…

A: (a)The relative position vector pointing from the planet to the star is,Substitute the values,

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A: Point 1: Here we can take the certain corner as origin. So the coordinates of the origin is O(0 ,…

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

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Q: Q. 9: Find the direction cosines of cartesian coordinates (4, -1, 2).

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A: Given is  original frame {A} FIRSTLY  Frame is rotated along X axis with angle 13 degree  then…

Q: A force F of 36N acts on a box in the direction of the vector OP, where P (-5,7,–3) and O(0, 0, 0).…

A: The direction vector can be represented as, Here, (x­1, y1, z1) and (x­2, y2, z2) represent the…

Q: Problem 1. Consider the Sun-Earth system with a center-to-center distance of 1.5x 101 m. Suppose…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: R h

A: Given, R=5.05m thickness, t=10.1×10-3m ρr=1.39r kg/m3 So, the mass is given by m=2πt∫0Rr.ρrdr

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Q: A position-time graph for a particle moving along the x axis is shown in the figure below. x (m) 12…

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.