A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 38 rad/s. The wheel is run at that angular velocity for 30 s and then power is shut off. The wheel slows down uniformly at 2.1 rad/s2 until the wheel stops. In this situation, the angular acceleration of the wheel between t = 0 s and t = 10 s is

The angular acceleration of the grinding wheel at the given time interval is 3.8 rad/s^2

Explanation:

Given:

Initial time of the grinding wheel, t1 = 0

final time of the grinding wheel, t2 = 10 s

Initial angular velocity of the grinding wheel, u = 0

final angular velocity of the grinding wheel, v = 38 rad/s

The angular acceleration of the wheel between t = 0 s and t = 10 s, is calculated as;

a = dv/dt

Where;

a is angular acceleration

dv is change in angular velocity = v - u = 38 - 0 = 38 rad/s

dt is change in time = t2 - t1 = 10 -0 = 10

a = 38 / 10

a = 3.8 rad/s^2

Therefore, the angular acceleration of the grinding wheel at the given time interval is 3.8 rad/s^2

If you run your boat aground, the first thing you should do is to calmly assess the situation. In case you have passengers on your boat, you should have them don PFDs (personal flotation devices). Afterwards, you should turn off the engine, check if there is any damage, and generally see if everything is okay.