1. **State the problem:** We are given a larger wheel with radius $R=88$ cm rotating at 210 revolutions per minute (rpm). We need to find its angular speed in radians per second. 2. **Formula and explanation:** Angular speed in radians per second is related to revolutions per minute by the formula: $$\omega = \text{rpm} \times \frac{2\pi \text{ radians}}{1 \text{ revolution}} \times \frac{1 \text{ minute}}{60 \text{ seconds}}$$ This converts revolutions per minute to radians per second. 3. **Calculate angular speed:** $$\omega = 210 \times \frac{2\pi}{60} = 210 \times \frac{\cancel{2}\pi}{\cancel{60}} \times \frac{1}{1}$$ Simplify the fraction: $$\frac{2}{60} = \frac{1}{30}$$ So, $$\omega = 210 \times \frac{\pi}{30}$$ Cancel common factors: $$210 = 7 \times 30$$ Therefore, $$\omega = \cancel{7 \times 30} \times \frac{\pi}{\cancel{30}} = 7\pi$$ 4. **Final answer:** The angular speed of the larger wheel is $$\boxed{7\pi \text{ radians per second}}$$ This is an exact answer in terms of $\pi$ as requested.