Physics

Moment of Inertia

39 Questions

The moment of inertia measures the resistance of a rigid body to changes in its rotational motion. Questions cover calculating inertia for uniform cylinders, solid spheres, and thin spherical shells. This core physics topic is vital for engineering aspirants and civil services preliminary tests.

Uniform cylinder inertiaSolid sphere inertiaAngular momentum equationRigid body rotationPoint mass inertia

Moment of Inertia Questions

Multiple choice

What is the moment of inertia of a hollow disk of mass M, outer radius R1, inner radius R2, and thickness t about an axis perpendicular to the disk and passing through its center?

  1. (1/2)M(R1^2 + R2^2) + (1/12)Mt^2

  2. (1/3)M(R1^2 + R2^2) + (1/12)Mt^2

  3. (1/4)M(R1^2 + R2^2) + (1/12)Mt^2

  4. (1/6)M(R1^2 + R2^2) + (1/12)Mt^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a hollow disk about an axis perpendicular to the disk and passing through its center is given by I = (1/2)M(R1^2 + R2^2) + (1/12)Mt^2.

Multiple choice

What is the moment of inertia of a solid sphere of mass M and radius R about an axis tangent to the sphere and passing through its center?

  1. (7/5)MR^2

  2. (2/3)MR^2

  3. (3/4)MR^2

  4. (4/5)MR^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a solid sphere about an axis tangent to the sphere and passing through its center is given by I = (7/5)MR^2.

Multiple choice

The angular momentum of a particle is given by the equation (L = I\omega), where (I) is the moment of inertia and (\omega) is the angular velocity. What is the moment of inertia of a point mass (m) rotating in a circular path of radius (r)?

  1. \(mr^2\)
  2. \(m\)
  3. \(\frac{m}{r^2}\)
  4. \(\frac{1}{mr^2}\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a point mass rotating in a circular path is given by (I = mr^2).

Multiple choice

What is the moment of inertia of a thin rod of mass (m) and length (L) about an axis perpendicular to the rod and passing through one end?

  1. \(\frac{1}{3}mL^2\)
  2. \(\frac{1}{2}mL^2\)
  3. \(mL^2\)
  4. \(2mL^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a thin rod about an axis perpendicular to the rod and passing through one end is given by (\frac{1}{3}mL^2).

Multiple choice

What is the moment of inertia of a uniform disk of mass (m) and radius (R) about an axis perpendicular to the disk and passing through its center?

  1. \(\frac{1}{2}mR^2\)
  2. \(mR^2\)
  3. \(2mR^2\)
  4. \(\frac{1}{4}mR^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a uniform disk about an axis perpendicular to the disk and passing through its center is given by (\frac{1}{2}mR^2).

Multiple choice

What is the moment of inertia of a uniform sphere of mass (m) and radius (R) about an axis passing through its center?

  1. \(\frac{2}{5}mR^2\)
  2. \(\frac{3}{5}mR^2\)
  3. \(\frac{4}{5}mR^2\)
  4. \(\frac{1}{5}mR^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a uniform sphere about an axis passing through its center is given by (\frac{2}{5}mR^2).

Multiple choice

What is the moment of inertia of a uniform cylinder of mass (m) and radius (R) about an axis parallel to the cylinder's axis and passing through its center?

  1. \(\frac{1}{2}mR^2\)
  2. \(mR^2\)
  3. \(2mR^2\)
  4. \(\frac{1}{4}mR^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a uniform cylinder about an axis parallel to the cylinder's axis and passing through its center is given by (\frac{1}{2}mR^2).

Multiple choice

What is the moment of inertia of a uniform rectangular plate of mass (m), width (w), and height (h) about an axis perpendicular to the plate and passing through its center?

  1. \(\frac{1}{12}m(w^2 + h^2)\)
  2. \(\frac{1}{2}m(w^2 + h^2)\)
  3. \(m(w^2 + h^2)\)
  4. \(2m(w^2 + h^2)\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a uniform rectangular plate about an axis perpendicular to the plate and passing through its center is given by (\frac{1}{12}m(w^2 + h^2)).

Multiple choice

What is the moment of inertia of a uniform triangular plate of mass (m), base (b), and height (h) about an axis perpendicular to the plate and passing through its vertex?

  1. \(\frac{1}{12}mb^2\)
  2. \(\frac{1}{2}mb^2\)
  3. \(mb^2\)
  4. \(2mb^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a uniform triangular plate about an axis perpendicular to the plate and passing through its vertex is given by (\frac{1}{12}mb^2).