Question

Continuous Assessment 3 MRDB/3Q Exercise 3. An axisymmetric body of uniform density $d$ consists of the region $ar^3 \le z \le 2aR^3 - ar^3$, $r \le R$ in cylindrical polar coordinates. Calculate the total mass $M$ in terms of $a$, $d$ and $R$ only. Calculate the centre of mass $\bar{x}$ and the components of the moment of inertia tensor $I_G$ about the centre of mass with respect to the Cartesian basis vectors in terms of $a$, $R$ and $M$ only.

          Continuous Assessment 3
MRDB/3Q
Exercise 3.
An axisymmetric body of uniform density $d$ consists of the region
$ar^3 \le z \le 2aR^3 - ar^3$, $r \le R$
in cylindrical polar coordinates.
Calculate the total mass $M$ in terms of $a$, $d$ and $R$ only. Calculate the centre of mass $\bar{x}$ and the components of the moment of inertia tensor $I_G$ about the centre of mass with respect to the Cartesian basis vectors in terms of $a$, $R$ and $M$ only.

Continuous Assessment 3
MRDB/3Q
Exercise 3.
An axisymmetric body of uniform density d consists of the region
ar^3 ≤ z ≤ 2aR^3 - ar^3, r ≤ R
in cylindrical polar coordinates.
Calculate the total mass M in terms of a, d and R only. Calculate the centre of mass x̅ and the components of the moment of inertia tensor IG about the centre of mass with respect to the Cartesian basis vectors in terms of a, R and M only.

Added by Julie B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Jaya M

Step 1

To calculate the mass, we need to integrate the density over the volume of the body. In cylindrical polar coordinates, the volume element is given by dV = r dr dz dθ, where r is the radial distance, dz is the height, and dθ is the angle. The density is given as Show more…

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Please answer clearly with full working and explanation. MRDB/3Q Continuous Assessment 3 Exercise 3. An axisymmetric body of uniform density d consists of the region \[ar^3z^2aR^3-ar^3rR\] in cylindrical polar coordinates. Calculate the total mass M in terms of a, d, and R only. Calculate the center of mass x and the components of the moment of inertia tensor I_g about the center of mass with respect to the Cartesian basis vectors in terms of a, R, and M only.