Equation of motion angular acceleration

A question is this type if and only if it asks for the angular acceleration of a rotating body at a specific instant by applying the rotational equation of motion (torque = I × angular acceleration), without requiring energy methods.

3 questions · Standard +0.9

Sort by: Default | Easiest first | Hardest first
CAIE FP2 2012 November Q2
7 marks Standard +0.8
2 \includegraphics[max width=\textwidth, alt={}, center]{34024618-0ff9-44a1-ac57-d4d7e8a3655e-2_431_421_881_861} A uniform disc of radius 0.4 m is free to rotate without friction in a vertical plane about a horizontal axis through its centre. The moment of inertia of the disc about the axis is \(0.2 \mathrm {~kg} \mathrm {~m} ^ { 2 }\). One end of a light inextensible string is attached to a point on the rim of the disc and the string is wound round the rim. The other end of the string is attached to a particle of mass 1.5 kg which hangs freely (see diagram). The system is released from rest. Find
  1. the angular acceleration of the disc,
  2. the speed of the particle when the disc has turned through an angle of \(\frac { 1 } { 6 } \pi\).
CAIE FP2 2012 November Q2
7 marks Standard +0.8
2 \includegraphics[max width=\textwidth, alt={}, center]{d3e9a568-a9ea-483e-8e65-90fdc4a69781-2_431_421_881_861} A uniform disc of radius 0.4 m is free to rotate without friction in a vertical plane about a horizontal axis through its centre. The moment of inertia of the disc about the axis is \(0.2 \mathrm {~kg} \mathrm {~m} ^ { 2 }\). One end of a light inextensible string is attached to a point on the rim of the disc and the string is wound round the rim. The other end of the string is attached to a particle of mass 1.5 kg which hangs freely (see diagram). The system is released from rest. Find
  1. the angular acceleration of the disc,
  2. the speed of the particle when the disc has turned through an angle of \(\frac { 1 } { 6 } \pi\).
OCR M4 2002 January Q4
8 marks Challenging +1.2
4 A uniform circular disc has mass \(m\), radius \(a\) and centre \(C\). The disc is free to rotate in a vertical plane about a fixed horizontal axis passing through a point \(A\) on the disc, where \(C A = \frac { 1 } { 3 } a\).
  1. Find the moment of inertia of the disc about this axis. The disc is released from rest with \(C A\) horizontal.
  2. Find the initial angular acceleration of the disc.
  3. State the direction of the force acting on the disc at \(A\) immediately after release, and find its magnitude.