Rigid Body Dynamics

Question 1 Multiple Choice (Single Answer)

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?

\(\frac{1}{3}mL^2\)
\(\frac{1}{2}mL^2\)
\(mL^2\)
\(2mL^2\)

Question 2 Multiple Choice (Single Answer)

What is the angular momentum of a rigid body rotating about a fixed axis with angular velocity (\omega) and moment of inertia (I)?

\(I\omega\)
\(\frac{1}{2}I\omega^2\)
\(2I\omega\)
\(\frac{1}{2}I\omega\)

Question 3 Multiple Choice (Single Answer)

What is the kinetic energy of a rigid body rotating about a fixed axis with angular velocity (\omega) and moment of inertia (I)?

\(\frac{1}{2}I\omega^2\)
\(I\omega\)
\(2I\omega^2\)
\(\frac{1}{2}I\omega\)

Question 4 Multiple Choice (Single Answer)

What is the torque acting on a rigid body rotating about a fixed axis with angular acceleration (\alpha) and moment of inertia (I)?

\(I\alpha\)
\(\frac{1}{2}I\alpha^2\)
\(2I\alpha\)
\(\frac{1}{2}I\alpha\)

Question 5 Multiple Choice (Single Answer)

What is the equation of motion for a rigid body rotating about a fixed axis?

\(I\alpha = \sum\tau\)
\(\frac{1}{2}I\alpha^2 = \sum\tau\)
\(2I\alpha = \sum\tau\)
\(\frac{1}{2}I\alpha = \sum\tau\)

Question 6 Multiple Choice (Single Answer)

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?

\(\frac{1}{2}mR^2\)
\(mR^2\)
\(2mR^2\)
\(\frac{1}{4}mR^2\)

Question 7 Multiple Choice (Single Answer)

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

\(\frac{2}{5}mR^2\)
\(\frac{3}{5}mR^2\)
\(\frac{4}{5}mR^2\)
\(\frac{1}{5}mR^2\)

Question 8 Multiple Choice (Single Answer)

What is the angular velocity of a rigid body rotating about a fixed axis with constant angular acceleration (\alpha) and initial angular velocity (\omega_0) after time (t)?

\(\omega_0 + \alpha t\)
\(\omega_0 - \alpha t\)
\(2\omega_0 + \alpha t\)
\(\frac{1}{2}\omega_0 + \alpha t\)

Question 9 Multiple Choice (Single Answer)

What is the angular displacement of a rigid body rotating about a fixed axis with constant angular acceleration (\alpha) and initial angular velocity (\omega_0) after time (t)?

\(\omega_0 t + \frac{1}{2}\alpha t^2\)
\(\omega_0 t - \frac{1}{2}\alpha t^2\)
\(2\omega_0 t + \alpha t^2\)
\(\frac{1}{2}\omega_0 t + \alpha t^2\)

Question 10 Multiple Choice (Single Answer)

What is the relationship between the linear velocity (v) of a point on a rigid body rotating about a fixed axis and the angular velocity (\omega) of the body?

\(v = \omega r\)
\(v = \frac{1}{2}\omega r\)
\(v = 2\omega r\)
\(v = \frac{1}{4}\omega r\)

Question 11 Multiple Choice (Single Answer)

What is the relationship between the centripetal acceleration (a_c) of a point on a rigid body rotating about a fixed axis and the angular velocity (\omega) of the body?

\(a_c = \omega^2 r\)
\(a_c = \frac{1}{2}\omega^2 r\)
\(a_c = 2\omega^2 r\)
\(a_c = \frac{1}{4}\omega^2 r\)

Question 12 Multiple Choice (Single Answer)

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?

\(\frac{1}{2}mR^2\)
\(mR^2\)
\(2mR^2\)
\(\frac{1}{4}mR^2\)

Question 13 Multiple Choice (Single Answer)

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?

\(\frac{1}{12}m(w^2 + h^2)\)
\(\frac{1}{2}m(w^2 + h^2)\)
\(m(w^2 + h^2)\)
\(2m(w^2 + h^2)\)

Question 14 Multiple Choice (Single Answer)

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?

\(\frac{1}{12}mb^2\)
\(\frac{1}{2}mb^2\)
\(mb^2\)
\(2mb^2\)

Questions