Revisica
Sign in
ENGR5004 / Week 9
Dynamics L17 Worked example 2TutorialOld spec ENGR216Third8 min

ENGR216 Dynamics L17 worked example 2 (slides 14-15) official answers

The 50 kg pendulum of a Charpy impact machine rotates about a fixed pin A. Its centre of mass G is 1.25 m from A, and its radius of gyration about A is kA=1.75k_A = 1.75 m. It is released from rest with θ=0\theta = 0, where θ\theta is the angle of AG below the horizontal. Neglect friction; take g=9.81g = 9.81 m/s2^2.

Find the angular velocity of the pendulum when θ=90∘\theta = 90^\circ (AG vertical, G directly below A).

Charpy impact machine: pendulum pivoted at A, G 1.25 m from A, theta measured downwards from the horizontal; the specimen S sits below A.
Charpy impact machine: pendulum pivoted at A, G 1.25 m from A, theta measured downwards from the horizontal; the specimen S sits below A.
Formulas you may need
  • Principle of work and energy: T1+∑U1−2=T2T_1 + \sum U_{1-2} = T_2 (learn this)
  • Fixed-axis rotation: T=12IAω2T = \tfrac12 I_A\omega^2, IA=mkA2I_A = m k_A^2 (learn this)
  • Work of the weight: U=mg ΔyU = mg\,\Delta y for a drop Δy\Delta y of G (learn this)