Moment of Inertia of Solid Sphere and Thin Spherical Shell

What is the pressure at a point P at depth h below the surface of a liquid of uniform density?

hρg

If the free surface of the liquid is open to the atmosphere, what is the absolute pressure within the liquid at a depth h?

p0 - hρg

What is the definition of angular Simple Harmonic Motion (SHM)?

The oscillatory motion of a body where restoring torque is directly proportional to angular displacement.

What is the differential equation of angular Simple Harmonic Motion (SHM)?

(I - ct) d^2θ/dt^2 = 0 Signup and view all the answers

What does the moment of inertia of a solid sphere depend on?

Radius and density Signup and view all the answers

What is the moment of inertia of a thin spherical shell?

(2/3)MR^2 Signup and view all the answers

What happens to the moment of inertia of a ballet dancer when she stretches her arms during a spin?

Increases Signup and view all the answers

If a hollow cylinder and a solid cylinder of the same radius rotate about their respective cylinder axes, how do their moments of inertia compare?

Moment of inertia of the hollow cylinder is greater than the solid cylinder Signup and view all the answers

What is the effect on the duration of a day if the Earth suddenly shrinks while keeping its mass constant?

Day duration decreases Signup and view all the answers

In a circular disc and a circular ring with the same radii rotating about a tangential axis in their planes, how do their radii of gyration compare?

Radii of gyration of the ring is greater than the disc Signup and view all the answers

If a ballet dancer's angular speed decreases while stretching her arms in a turn, what happens to her linear speed?

Decreases Signup and view all the answers

When comparing the moment of inertia of a solid sphere to that of a thin spherical shell, which one is generally larger?

Moment of inertia of solid sphere is larger Signup and view all the answers

What is the formula for the moment of inertia of a solid sphere about an axis passing through its centre?

$\frac{2}{5}MR^2$ Signup and view all the answers

What is the expression for the moment of inertia of a thin spherical shell about its diameter?

$\frac{2}{3}MR^2$ Signup and view all the answers

Why do a uniform disc and a hollow right circular cone have the same formula for moment of inertia for rotation about their corresponding central symmetry axes?

The distribution of mass about the respective central symmetry axes is the same. Signup and view all the answers

How does the moment of inertia of a hollow right circular cone compare to that of a disc?

Both have equal moments of inertia. Signup and view all the answers

In the expression for the moment of inertia of a thin spherical shell about its diameter, what does $h$ represent?

Distance between two axes Signup and view all the answers

What is used to calculate the moment of inertia about an axis parallel to the diameter for a thin spherical shell?