How many degrees of freedom f does a rigid body have (that is, how many independent coordinates are required to uniquely determine its position in space at a given instant): (a) In rotation about an axis that is fixed in space? (b) In translation? (c) In two-dimensional (planar or laminar) motion? (d) In general?

Q: velocity of the proton in units of km/s

A: Given: Mass of proton is m=1.673×10-27 kg Charge on proton is q=1.6×10-19 C Radius of path is r=4.46…

Q: The H2S molecule contains two hydrogen atoms and one sulfur atom. The position vectors of the…

A: Given:  rH1→ = 0.7i^+1.01j^+0.00k^rH2→ = 0.7i^ -1.01j^+0.00k^rS→ = 0.00i^+0.00j^+0.00k^Mass of H = 1…

Q: Two concentric spherical shells with uniformly distributed masses M₁ = 687 kg and M₂ = 239 kg are…

A:

Q: 76. (a) The x-component of Jay's velocity (b) The angle Jay's position vector makes with the x axis…

A: A object moving in a circular motion has components of velocity in x- and y- direction. The only net…

Q: Q2: Solve the initial value problem by implementing the convolution: 4y" + y = g(t), y(0) = 3, y'(0)…

A: Given: 4y"+y=gt, y0=3, y'0=-7

Q: Three particles qı = 7.90 µC, q2 = -1.10 µC, and q3 = 2.00 µC, have Cartesian coordinates (0.00,…

A:

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

A:

Q: Very far from earth (at R=∞), a spacecraft has run out of fuel and its kinetic energy is zero. If…

A: Solution:Explanation:Mechanical energy includes both kinetic energy (energy due to motion) and…

Q: Discworld has radius R and mass M; the incompetent wizard Rincewind has mass m and levitates at…

A:

Q: Three disks A, B, and C with same radius 5.0 cm are placed at coordinate (0,50 cm), (-15 cm, 0), and…

A:

Q: (c) Two uniform stars are separated by 2.36 × 1016 m. The star on the left has a mass of 5.33 × 1028…

A: The magnitude of gravitational force on an object having mass m due to mass M is given by Where G =…

Q: A solid sphere of uniform density has a mass of 3.2 x 104 kg and a radius of 0.50 m. What is the…

A:

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

A:

Q: Calculate the magnitude and the direction angle (in radians) for the vector <3,3sqrt3>.

A: The objective of the question is to find the magnitude and direction angle of the vector .

Q: Let 7 (t) = (4t? + 5, 5e-4, – 2 sin(t)) Find the unit tangent vector T (t) at the point t = 0 T(0) =…

A: Given-                                                                    r→t=4t2+5, 5e-4t,…

Q: Here are three displacements, each measured in me- ters: di = .0 and dz = 4.0î +3.0ĵ+2.0k. (a) What…

A:

Q: Consider two iron spheres, each of diameter 195 mm, which are just touching. At what distance r from…

A:

Q: This quesfion will require you to sketch out a thing. (Or at least I highly recommend you do it to…

A: Consider the free-body diagram of the package as follows.

Q: 12. Express in cartesian components: (a) the vector G'extending from the origin to the mid- point of…

A:

Q: The cartesian coordinate form of two vectors are: (-2, 0, 2) and (1, 1, 1). Find the angle between…

A: Given: The cartesian coordinate of the vectors is (x1, y1, z1)=(-2, 0, 2) and (x2, y2, z2)=(1, 1,…

Q: Two points in the xy plane have Cartesian coordinates (5.50, -7.00) m and (-6.50, 6.50) m. (a)…

A:

Q: Sphere A with mass 89 kg is located at the origin of an xy coordinate system; sphere B with mass 58…

A:

Q: Find the average and

A: from the given conditions  we find average deviation-

Q: Two disks each have a mass of 5 kg and a radius 300 mm. They spin as shown at the rate of w1 = 1200…

A: Given: Two disks each have a mass of 5 kg and a radius 300 mm. They spin as shown at the rate of w1…

Q: (a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an…

A: (a) In particular, we're using the principle of conservation of mechanical energy, which states that…

Q: HE Problem 9: Consider the sign shown in the figure, which has a mass of m= 8.2 kg. sin() cos()…

A:

Q: Given the points A(2, -1, -3) and B(1, 3, 4), specify the vector at point A that extends to point B…

A:

Q: Determine the y-component of unit vector parallel to the sum of vectors (-4.1)i + (5.9)j + (-7.9)k…

A: Given: The vectors are  (-4.1)i + (5.9)j + (-7.9)k and (8.3)i + (-8.4)j + (4.4)k.

Q: Sphere A with mass 70 kg is located at the origin of an xy coordinate system; sphere B with mass 73…

A:

Q: Two points in the Cartesian plane are A (3.90 m, -7.30 m) and B (-1.20 m, 1.30 m). Find the distance…

A:

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

A: Given that: The vector a is a=i+8j+4k The vector b is b=7i-6j-6k   It is required here to calculate…

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: 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: One model for a certain planet has a core of radius Rand mass M surrounded by an outer shell of…

A:

Q: The three vectors in the figure have magnitudes a = 2.60 m, b = 2.70 m, and c = 10.0 m and angle =…

A:

Q: given the position vectors r=(3,2,1) and r=(2,4,3), (a) Find a unit vector parallel to the resultant…

A:

Q: A solid ball ( I = 2/5 mr2 ) a mass of 2 kg and a radius of 4 cm is rolling (moves both…

A: Given: The mass of the sphere is 2 kg. The radius of the sphere is 4 cm. The height of the inclined…

Q: Three particles qi 7.20 µC, q2 = -8.50 µC, and q3 1.70 μC , (3) have Cartesian coordinates (0.00,…

A: We have 3 charges q1=7.2 uC, q2=-8.5 uC and q3=1.7 uC at positions (x,y)=(0,0), (4.7,0) and…

Q: Problem 1) We consider the following system when placed in a uniform gravitational field (with…

A: Here a simple mechanical system in which we have disc of radius a and pendulum of length l simple.…

Q: 1- (Exercise) Given the vectors A = Ti-2), B =i-3k, and C = 2i-2j+3k, calculate the fol- (1) lowing…

A: Given, A→=7i^-2j^B→=i^-3k^C→=2i^-2j^+3k^ d. A.→B→=A→B→cosθ…

Q: Newton's law of universal gravitation states that two particles exert a pull on each other with…

A: