Consider a cylindrical shell of constant density p, inner radius r₁, outer radius R, and heightH. Assume that the cylinder is oriented along the z-axis.(a) Find the mass, m, of the cylinder.(b) Show that the z-axis goes through the centre of mass of the cylinder The moment of inertia for a set of objects of mass m; rotating about a common axis isdefined as1 = Σm₁r?2where r, is the distance of the ith object to the axis of rotation. If there are many particlesthat make up a larger object then this sum transforms into an integral,4-fff or a.I =dV,Vwhere p is the mass density and V the volume of the object.In this exercise we will explore moment of inertia by rolling two objects down an inclineplane in the Experimental Math Lab Space.

Answered: Image /qna-images/answer/c464d80b-acdd-4943-a03c-e54d410a1d00.jpg

Answered: Consider a cylindrical shell of…

Similar questions

Find the center of mass of the thin half-disk whose region is bounded above by the semicircle and bounded below by the x axis. Take the y=√(1-x^2) and the density of the disk to be δ = 1.
Find the center of mass of a sphere of mass M and radius R and a cylinder of mass m, radius r, and height h arranged as shown below. Express your answers in a coordinate system that has the origin at the center of the cylinder. (Assume that the +x-axis is to the right, the +y-axis is up along the page, and the +z-axis is out of the page. Use any variable or symbol stated above as necessary.) (a) XCM = YCM = ZCM = (b)
Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density or densities. (Hint: Some of the integrals are simpler in polar coordinates.) m = y = x² y = 0 X = 4 P = (x, y) = ( kxy
A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 86.2 × 105 kg, of which 14.7 × 105 kg is fuel. The rocket engine is then fired for 180 s, during which fuel is consumed at the rate of 480 kg/s. The speed of the exhaust products relative to the rocket is 2.98 km/s. (a) What is the rocket's thrust? After the 180 s firing, what are (b) the mass and (c) the speed of the rocket?
A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 75.8 x 105 kg, of which 15.3 × 105 kg is fuel. The rocket engine is then fired for 410 s, during which fuel is consumed at the rate of 390 kg/s. The speed of the exhaust products relative to the rocket is 2.81 km/s. (a) What is the rocket's thrust? After the 410 s firing, what are (b) the mass and (c) the speed of the rocket? (a) Number i Units (b) Number i Units (c) Number i Units
A water molecule consists of an oxygen atom and two hydrogen atoms. The two O—H bonds are each0.1 nm long and form an angle of 107◦ with each other. Where is the molecule’s centre of mass located?Consider the mass of the oxygen atom to be 16 times the mass of a hydrogen atom, and place yourhydrogen atoms along the x-axis of your coordinate system. [Hint: Draw your coordinate system!].
Problem 3: (a) Use spherical coordinates to find the center of mass (CM) of a uniform solid hemisphere of radius R, whose flat face lies in the ry plane with its center on the origin. [Note: dV = ² sin 0 dr do do.] (b) Use your result from part (a) to calculate the CM of a hemispherical "bowl" with outer radius R and inner radius kR, k < 1. (Depending on your work in part (a), you may not even need to do another integral.) (c) Use your result from the previous part to find the CM for an infinitely thin hemispherical shell of radius R.
What’s the center of mass for each situation?
A firework with mass M is launched from the origin with initial speed v0 and angle θ0 and travels along the usual parabolic path above flat ground. At the peak of its path, it explodes into two pieces. Piece one has mass .5M and speed v1 in an angle of 30◦ below the horizontal direction and the other piece has mass .5M and speed v2 in an unknown direction. (a) Do the two pieces land at the same time? (Justify your answer) (b) Sketch the motion of the COM and of both pieces. Note any external forces, and describe if p is conserved in x, y or both for the duration of the flight. Also note if the two pieces land at the same distance from the target or describe which one lands closer/further.
Problem 3: A particle with mass ma = 3.00 kg is located at ra = (2.50 i + 3.50 j) m, and a second particle of mass m2B = 5.00 kg is located at rB = (1.50 i - 3.00 j) m. Find the location of the center of mass of the system relative to the point (1,1).
Determine the center of mass of a uniform cone of height h and radius R, with its axis pointing along z. (Hints: What is the CM in x and y? Let λ by the mass density per unit volume, and find the mass of the thin disk shown in the drawing. How is r/z related to R/h?)
A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 78.4 × 105 kg, of which 8.68 × 105 kg is fuel. The rocket engine is then fired for 340 s, during which fuel is consumed at the rate of 340 kg/s. The speed of the exhaust products relative to the rocket is 3.78 km/s. (a) What is the rocket's thrust? After the 340 s firing, what are (b) the mass and (c) the speed of the rocket? (a) Number 1290000 Units N (b) Number 7720000 Units kg (c) Number 3830 Units m/s

SEE MORE QUESTIONS

Consider a cylindrical shell of constant density p, inner radius 7₁, outer radius R, and height H. Assume that the cylinder is oriented along the z-axis. (a) Find the mass, m, of the cylinder. (b) Show that the z-axis goes through the centre of mass of the cylinder