Question

A uniform disk is constrained to rotate about an axis passing through its center and perpendicular to the plane of the disk. If the disk starts with an angular velocity of 7.0 rad/s and is subject to a constant angular acceleration of 3.0 rad/s2, find the angular displacement of a point on the rim of the disk as it rotates under these conditions for 15 s. (Assume the positive direction is in the initial direction of the rotation of the disk. Indicate the direction with the sign of your answer.)

Answer 1

442.5 rad

Step-by-step explanation:

w₀ = initial angular velocity of the disk = 7.0 rad/s

α = Constant angular acceleration = 3.0 rad/s²

t = time period of rotation of the disk = 15 s

θ = angular displacement of the point on the rim

Angular displacement of the point on the rim is given as

θ = w₀ t + (0.5) α t²

inserting the values

θ = (7.0) (15) + (0.5) (3.0) (15)²

θ = 442.5 rad