An electric fan with blades of length 0.4 m starts from rest. It reaches a steady rotational speed of 300 rpm in 5 s with uniform angular acceleration. The tangential acceleration of a point at the tip of the blade is:

Step-by-step solution

Given, initial angular speed ₀ = 0 Final angular speed = 300 rpm Time t = 5 s Radius of the circular path of the tip R = 0.4 m First, convert the final angular speed into rad s ⁻¹ : = 300 2 60 rad s ⁻¹ = 10 rad s ⁻¹ Calculate the angular acceleration using the first equation of rotational kinematics: = - ₀ t = 10 - 0 5 = 2 rad s ⁻² The tangential acceleration a_t is related to angular acceleration by the formula: a_t = R a_t = 2 0.4 = 0.8 m s ⁻² Answer: 0.8 m s ⁻²