AP Physics C: Mechanics 6.1 Rotational Kinetic Energy Questions

Relate rotational kinetic energy to rotational inertia and angular velocity, compare it with translational energy, and apply conservation to rotating systems.

Exam points

calculate rotational kinetic energy from system inertia and angular speed
apply mechanical-energy conservation to solve angular speed or a rotating point's linear speed
separate centre-of-mass translation from rotation when accounting for total kinetic energy
equate energy dissipated by a retarding force to the loss of rotational kinetic energy
combine torque, duration and inertia to express a rotating system's final kinetic energy

Covered syllabus points

6.1.A—Describe the rotational kinetic energy of a rigid system in terms of the rotational inertia and angular velocity…

[Maximum number: 4]

Object A is a long, thin, uniform rod of mass M and length 2 L that is free to rotate about a pivot of negligible friction at its left end, as shown above.

Derive an expression for the angular speed of object B when it is in the position shown above. Express your answer in terms of $M, L, I_{\mathrm{B}}$ , and physical constants, as appropriate.

Note: Figure not drawn to scale.

For using conservation of energy
$U_{g 1}=K_{2}$

1 point

For correctly relating the change in rotational kinetic energy to the change in gravitational potential energy
$m g h=\frac{1}{2} I \omega^{2}$

1 point

For correctly substituting for h into the equation above
$m g\left(\frac{L}{2}\right)=\frac{1}{2} I \omega^{2}$

1 point

For an expression for $\omega$ that uses only the allowed symbols and is algebraically consistent with the previous steps
$\begin{aligned} \omega=\sqrt{\frac{2 m g h}{I}}=\sqrt{\frac{2 M g(L / 2)}{I_{\mathrm{B}}}} \omega=\sqrt{\frac{M g L}{I_{\mathrm{B}}}} \end{aligned}$

1 point

Total for part (f)

for question 215 points

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Covered syllabus points

Question 1