An oceanographic probe is lowered into the sea using a light, high-strength cable wrapped around a solid cylindrical drum winch. The free end of the cable is attached to the probe of mass 1.8 kg1.8\text{ kg}1.8 kg.
Initially, the drum is locked and the probe is held stationary.
The drum is then released so that the probe descends vertically, causing the drum to rotate about its fixed central axle. As the probe falls, the cable unwinds from the drum without slipping.
The linear velocity vvv of the descending probe is related to the angular velocity ω\omegaω of the drum by v=rωv = r\omegav=rω, where rrr is the radius of the drum.
The probe accelerates uniformly as it falls from rest. The cable remains taut and has negligible thickness and mass.
When the probe has descended a distance of 1.5 m1.5\text{ m}1.5 m, its linear velocity is VVV.
Calculate VVV by considering the energy transfers that occur during the descent.
Take g=9.81 m s−2g = 9.81\text{ m s}^{-2}g=9.81 m s−2.
Once the probe reaches the sea floor, the winch motor is decoupled and the drum continues to spin freely in a loose loop of cable.
The bearings of the drum apply a constant frictional torque of 1.2×10−2 N m1.2 \times 10^{-2}\text{ N m}1.2×10−2 N m to its axle.
The angular velocity of the drum at the moment the probe lands is 80 rad s−180\text{ rad s}^{-1}80 rad s−1.
Determine, in rad\text{rad}rad, the total angle turned through by the drum during the first 12.0 s12.0\text{ s}12.0 s after the probe lands.
8 exam-style questions on AQA A Level Physics Rotational dynamics (A-level only), covering Concept of moment of inertia (A-level only), Rotational kinetic energy (A-level only), Rotational motion (A-level only), Torque and angular acceleration (A-level only), Angular momentum (A-level only), and Work and power (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.