This is the boss. No calculator, and the numbers are pinned to fit in your head. Two shop conveniences make that honest rather than artificial. The speed is quoted in radians per second, so no 2π/60 is needed. And the polar moment uses the trade's own rule, $J \approx 0.1\,d^{4}$ — the exact value is $\pi d^{4}/32 = 0.0982\,d^{4}$, so the rule is inside 2%, and every engineer who has ever sized a shaft on the back of a drawing has used it.

One drive line, four lines of working, and every answer feeds the next: power and speed give the torque, the diameter gives J, torque and J give the shaft's surface stress, and the torque again gives the key's stress. Write each line down as you go — one early slip rolls all the way to the hub.

Then read what the last line actually asks. It does not want a fifth number; it wants a decision — signed off, or rejected — the way a real check ends. The arithmetic is only there to earn you the right to make it. Everything in the chapter rides in this one line. 5★ under par here is the chapter crown. Clock in.