Question

A cylinder of mass 5 kg and radius 30 cm and free to rotate about its axis receives an angular impulse of 3 kg metre square per second initially followed by a similar impulse after every 4 second what is the angular speed of cylinder 30 second after the initial impulse the cylinder is at rest initially

Answer 1

Explanation:

Given A cylinder of mass 5 kg and radius 30 cm and free to rotate about its axis receives an angular impulse of 3 kg metre square per second initially followed by a similar impulse after every 4 second what is the angular speed of cylinder 30 second after the initial impulse the cylinder is at rest initially

• We know that angular impulse is given by Δ L
•                                                 So 3 = Lf – Li
•                                   Now L = I ω
•                                           3kg m^2/s  = mR^2 / 2 ω
•                             Or ω = 6 / mR^2
•                                        = 6 / 5 x (0.3)^2
•                                        = 6 x 20 / 9
•                                        = 40 / 3 rad / s
•                   Now L = I ω
•                          3 = I (ωf – ωi )
•                 So 3 / I = ωf – ωi  (but 3/I = 40/3)
•      So ωf = ωi + 3/I
•       So ωf = ωi + 40/3
• Now t = 0,
• So ω = 40 / 3
• At t = 4,
• So ω = 40/3 + 40/3
•         = 80 / 3
• Since tωe impulse is imparted after every 4 secs. Impulses are imparted at 4,8,12,16,20,24,28 and last one lasts up to t = 32 s
• So ωf = 8 x 40 / 3
•         = 320 / 3 rad / s
•         = 106.66 rad / s

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