A solid cylinder rotates about its axis from rest with a constant angular acceleration. If the angle it rotates during the 3^ rd second of its motion is 20 rad, the angular velocity of the cylinder at the end of the 4^ th second is :

Step-by-step solution

Let the constant angular acceleration be . The angle rotated during the n^ th second is given by: _n = ₀ + 2 (2n - 1) Given that the cylinder starts from rest ( ₀ = 0 ) and ₃ = 20 rad for n = 3 : 20 = 0 + 2 (2(3) - 1) 20 = 5 2 = 8 rad/s ^2 The angular velocity at the end of the 4^ th second ( t = 4 s) is: = ₀ + t = 0 + 8 4 = 32 rad/s Answer: 32 rad/s