A hollow cylindrical drum of radius 0.5 m is placed inside an elevator that is accelerating upwards at 5 m s ⁻² . A block is in contact with the inner vertical wall of the drum. The coefficient of static friction between the block and the wall is 0.2 . If the drum rotates about its vertical axis, what is the minimum angular velocity required to keep the block stationary relative to the drum? (Take g = 10 m s ⁻² )

Step-by-step solution

In the frame of the accelerating elevator, the block experiences a downward pseudo force ma in addition to its weight mg . Effective downward force = m(g + a) = m(10 + 5) = 15m . The normal reaction N from the wall provides the necessary centripetal force: N = m ^2 R . To prevent the block from slipping downwards, the limiting static friction must balance the effective downward force: f_ max = N = m(g+a) . Substituting N : (m ^2 R) = m(g+a) = g+a R = 15 0.2 0.5 = 15 0.1 = 150 = 5 6 rad s ⁻¹ . Using only g instead o