A pottery wheel starts from rest and then begins to rotate with constant angular acceleration $0.57 \mathrm{rad} / \mathrm{s}^{2}$ for 17 seconds. In that time, what is the pottery wheel's angular displacement? 160 radians 82 radians 9.7 radians 110 radians

Step 1 ：We are given that a pottery wheel starts from rest and then begins to rotate with constant angular acceleration $0.57 \, \mathrm{rad/s^2}$ for 17 seconds. We are asked to find the pottery wheel's angular displacement.

Step 2 ：The formula for the angular displacement of an object moving with a constant angular acceleration is: \[\theta = \omega_0 t + \frac{1}{2} \alpha t^2\] where: \[\theta\] is the angular displacement, \[\omega_0\] is the initial angular velocity, \[t\] is the time, and \[\alpha\] is the angular acceleration.

Step 3 ：In this case, the pottery wheel starts from rest, so \[\omega_0 = 0\]. The angular acceleration \[\alpha\] is given as $0.57 \, \mathrm{rad/s^2}$ and the time \[t\] is given as $17 \, \mathrm{s}$. Substituting these values into the formula will give the angular displacement.

Step 4 ：Substituting the given values into the formula, we get: \[\theta = 0 \times 17 + \frac{1}{2} \times 0.57 \times (17)^2\]

Step 5 ：Solving the above expression, we get the angular displacement \[\theta = 82.365\] radians.

Step 6 ：Final Answer: The pottery wheel's angular displacement is \(\boxed{82.365}\) radians.