Two uniform solid spheres have the same mass of 1.95 kg, but one has a radius of 0.249 m and the other has a radius of 0.861 m. Each can rotate about an axis through its center. (a) What is the magnitude T of the torque required to bring the smaller sphere from rest to an angular speed of 267 rad/s in 18.3 s? (b) What is the magnitude F of the force that must be applied tangentially at the sphere's equator to give that torque? What are the corresponding values of (c) T and (d) F for the larger sphere? (a) Number (b) Number (c) Number HI I HI Units Units Units <> <>

Q: How do you express the coordinates of an object in cylindrical and spherical coordinates when its…

A: The Cartesian coordinates x,y,z of a point is related to cylindrical coordinate r,θ,z as, x=r cosθ,…

Q: If the Earth had twice the radius but the same density (assume constant density), then the…

A:

Q: part 3 of 3 In cases where we have radial symmetry about the origin (usually called spherical sym-…

A:

Q: While going down a roller coaster 20 m above the ground, a 100kg man is moving at 10 m/s  What is…

A:

Q: For some reason, I can't see how problem B was solved.

A:

Q: An electron with initial velocity vVo = 1.38 × 10° m/s enters a region 1.0 cm long where it is…

A: Given information Initial velocity of the electron u = 1.38 × 105 m/s Final velocity of the electron…

Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

A: To prove the shortest distance between two points is a straight line is explained as,

Q: spherical masses are always fun to observe and sort of analyze in physics. in this problem, we would…

A: Given, mass of the first spherical mass m1=49 kg mass of the second spherical mass m2=73 kg radius…

Q: you are asked to verify Kepler's Laws of Planetary Motion. For these exercises, assume that each…

A: Solution:

Q: Suppose that you plot the mass (y-axis, in g) versus volume (x-axis, in cm³) of 4 different…

A:

Q: If Earth orbits the Sun once per 365 days on a circular orbit with radius dEarth 1.5 × 10° km, what…

A: V = 2πdearth / T 365 days = 3.15 × 10⁷ sec

Q: d face to the blasting rockets, to the fuel gauge, and back to his worried expression as the engines…

A: The hero may have used the idea of conservation of momentum to achieve his aim (going back to his…

Q: Find the mass of the block 0 <x< 4,0 < y< 8,0 < z< 1, whose density 8, is given by 8 = 2 – z for 0)…

A: The density is given by: ρ=2-z The mass of the block is calculated as:…

Q: You have been assigned to a team charged with developing a plan to explore a new planetary body…

A: Given g=2.8 m/s2 specific gravity of oil=0.93 weight of oil=4 lbf

Q: Astronomers need to identify the position of objects in the sky with very high precision. For that,…

A: Solution: Let's consider the earth to be a spherical object. An imaginary line in the middle of the…

Q: This is a proportional reasoning calculation. You will want to set up equations, but mostly to look…

A:

Q: the field of view is flat, what is the resultant vector (yellow line) of an observer pointing his…

A: We know that we have given here as it moving 62 units 27° S of W to Jupiter, then finally moving to…

Q: Assume that each planet moves in an orbit given by the vectorvalued function r. Let r = || r||, let…

A:

Q: You drop a ball from a height h, and it takes a time t to reach the ground. Then you drop the same…

A: Time taken to fall from h is t ,  Time taken to fall from 2h is T  To find = Which of the statements…

Q: The 3X3 matrix which is being made is having axis coordinates, point coordinates and the force…

A: Axis coordinates, point coordinates, and the force coordinates

Q: Answer the following questions based on the Vector 1: 390 miles @ 22.6° N of East Vector 2: 336…

A: Vector 1 = 390 miles 22.6 N of eastVector 2 = 336 miles 59.6 W of NorthVector 3 = 80 miles due south

Q: There is a circle centered at the origin of a coordinate system S with radius R. Consider a…

A: Given data, Radius of the circle in the S- frame = R Velocity of S'- frame = v , at angle ϕ from the…

Q: Convert 7.8 from g/m3 to SI units.

A: Given data as per question            unit=7.8g/m3

Q: "Hey Gary, you know we should fill airliners with Helium to reduce their weight, saving millions of…

A: (b) Then given differential equation is,

Q: Problem 2.36 A hyperbolic earth departure trajectory has a perigee altitude of 250 km and a perigee…

A:

Q: M Rev A particle moves along a straight line such that its acceleration is a= (4t – 2) m/s², where t…

A: Given: a=4t2-2 m/s2at t=0 s ; x = -4 mat t=2 s ; x =-20 m

Q: If the Lagrange equation is in the following form z = =mR°ö² – mgRcoso L = what are the equations of…

A:

Q: Vector A = in spherical coordinate system at P(12, 12, 8).   What is the magnitude of vector A in…

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

Q: OK, same sort of track, but now with d = 3.05 m. Now suppose the blocks starts on the track at x =…

A:

Q: Write down the radius of the orbit of a satellite moving around the Earth if its height above the…

A: The radius of the orbit of a satellite moving around the Earth can be calculated using the following…

Q: nates of point N. 2) Write the vector KM in terms o

A:

Q: Calculate the acceleration due to the surface of earth ( radius of earth 8=64x105m) gravily at…

A: To find-Acceleration due to gravvity on earth's surface (g)=?Given that-Radius of earth (R)=6.4×106…

Q: Relate the cylindrical coordinates at a point to the spherical coordinates at the same point.

A:

Q: Calculate: V²[V•(F/r²)] and evaluate for r=1,25

A:

Q: To calculate: The distance covered by falling parachutist using Romberg integration, the parachutist…

A: Given: Velocity of the parachutist as function of time is, vt=gmc1-ec/mt g=9.8 m/s2 m=68.1 kg To…

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

A:

Q: Let's say we have a M1 and M2. Let's just say. Let's examine this hypothetical situation. The first…

A: When two masses M1 and M2 are placed at distance r , the gravitational force acts between both the…

Q: the properties of the dot product to show that for any vectors u and v. |u+v|²+ |u-v² = 2|u² +2|v|².…

A:

Q: Which of the following statements are correct? Adding two vectors creates a new "resultant" vector.…

A: from the given statements,we have to figure out correct statements.

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.