Question

A wheel of diameter 30.0 cm starts from rest and rotates with a constant angular acceleration of 2.50 rad/s2. At the instant the wheel has completed its second revolution, compute the radial acceleration of a point on the rim in two ways.  

Using the relationship arad = ω2r.  

From the relationship arad = v2/r.

Answer 1

a)

W_o = initial angular velocity = 0 rad/s

W_f = final angular velocity

= angular acceleration = 2.50 rad/s²

= angular displacement = 2 rad = 6.28 rad

using the equation

W_f² = W_o² + 2

W_f² = (0)² + 2 (2.50)(6.28)

W_f = 5.6 rad/s

r = radius = diameter /2 = 30 cm /2 = 15 cm = 0.15 m

a_rad = rW_f² = (0.15) (5.6)² = 4.7 m/s²

b)

V = rW_f = 0.15 x 5.6 = 0.84 m/s

a_rad = V²/r = (0.84)²/0.15 = 4.7 m/s²