Question

How to do question 4? All parts.

4 (2) pointn) Moment of inertia, Conservation of nngular momentuin, pendulum, Kinetic energy of rotation The physical peudulun in and the anghigtbly body L ily small body with nus muséi kx attached to the end of the rod. Initially the peuduluina iwal uu l rest. The tulet with iins mig2 g and velocity Vm m/s (dirested horiuntaly) hits the middle of the rod and sticks to it. XHrr the collision The pendn a) Motueut of inestia of the pendulum before the collnion ( point ,b) Moment of inertia of the system after the colision (2 point) the figure consists of the molid rod (diength L2 m and anu ma n4 ka) tas mo lun oscilliats. Find wed A pointa) the kinetic energy of the system (pendulun +bullet) before and after the colinion (5 fextra eredit) Period of oscillations of the penddulum ater the collision (G potnt) ne anu c) the angular veilocity of tlhe penudhulunm usnectisately ater the coflston (10 pholinte) eeit di speed 32 molecule L/2 average robable 2 s at cons

Answer 1

4

a)

I_i = initial moment of inertia before collision = (1/3) m_r L² + m₁ L² = (1/3) (4) (2)² + (6) (2)² = 29.33 kgm²

b)

I_f = Final moment of inertia after collision = (1/3) m_r L² + m₁ L² + m_B (L/2)² = (1/3) (4) (2)² + (6) (2)² + (2) (2/2)² = 31.33 kgm²

c)

using conservation of angular momentum

I_i w_i + m_B V_B (L/2) = I_f w_f

(29.33) (0) + (2) (5) (2/2) = (31.33)  w_f

w_f = 0.32 rad/s

d)

KE_i = kinetic energy before collision = (0.5) m_B V²_B = (0.5) (2) (5)² = 25 J

KE_f = kinetic energy after collision = (0.5) I_f w_f² = (0.5) (31.33) (0.32)² = 1.6 J