A wheel of radius 0.35 m starts from rest and reaches 150 rpm in 6.0 s, speeding up steadily…

Step 1. (a) $\alpha = \dfrac{15.71\ \text{rad/s}}{6.0\ \text{s}} = 2.618\ \text{rad/s}^2$.

Step 2. (b) $\theta = \tfrac12 \times 2.618\ \text{rad/s}^2 \times 36\ \text{s}^2 = 47.1\ \text{rad} = 7.5$ turns.

Step 3. (c) $v = 15.71\ \text{rad/s} \times 0.35\ \text{m} = 5.50\ \text{m/s}$; $a_t = 2.618\ \text{rad/s}^2 \times 0.35\ \text{m} = 0.916\ \text{m/s}^2$; $a_c = (15.71\ \text{rad/s})^2 \times 0.35\ \text{m} = 86.4\ \text{m/s}^2$.