Question

Notify Me Bookmark

Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone z = x2+y2, 1 ≤ z ≤ 4 if its density function is ρ(x,y,z) = 14−z.

Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone z = x2+y2, 1 ≤ z ≤ 4 if its density function is ρ(x,y,z) = 14−z.

Image text
Find the moment of inertia about the z -axis of a thin funnel in the shape of a cone z = x 2 + y 2 , 1 ≤ z ≤ 4 if its density function is ρ ( x , y , z ) = 14 − z .

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

A ballistic (m = 500 g) is traveling with a speed v0 = 5 m/s directly towards the middle of a thin rod⁡(M = 2 kg, L = 2 m), as shown below. The ballistic collides with and sticks to the rod, causing it to swing about a hinge at an angle ϕ, as shown below. The moment of inertia of a rod rotating about one of its ends is Irod = 13 ML2. Part (a) Which of the following quantities are conserved during the collision? (4 points) (a) Mechanical Energy (b) Linear Momentum (c) Angular Momentum (d) Net Force Part (b) Find the angular speed of the ballistic-rod system after the collision. (8 points) Part (c) Determine the maximum angle to which the ballistic and rod swing after the collision. (8 points) Part (d) If you wanted the ballistic and rod to swing higher, should you aim the ballistic higher or lower? Defend your reasoning with a conceptual argument. (5 points)
Solution
0 0

The coordinate axes in the figure run through the centroid of a solid wedge parallel to the labeled edges. The wedge has a = 4, b = 6, and c = 9. The solid has constant density δ = 1. The square of the distance from a typical point (x, y, z) of the wedge to the line L: z = 0, y = 6 is r2 = (y−6)2 + z2. Calculate the moment of inertia of the wedge about L. IL = (Simplify your answer. Type an integer or fraction.)
Solution
0 0

An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk's center, as in the figure below. The disk has mass 2.80 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.760 m long. (a) Find the ceiling fan's moment of inertia about a vertical axis through the disk's center. (Enter your answer in kg⋅m2.) kg⋅m2 (b) Friction exerts a constant torque of magnitude 0.119 N⋅m on the fan as it rotates. Find the magnitude of the constant torque provided by the fan's motor if the fan starts from rest and takes 15.0 s and 17.5 full revolutions to reach its maximum speed. (Enter your answer in N⋅m.) : N.m
Solution
0 0