Final answer:
The rotational acceleration is at a maximum at all times after t=0s. The maximum tangential acceleration of a point on the wheel a distance r=1.17m from its center is 8.1529 m/s^2. The total acceleration of the point can be calculated by combining the tangential acceleration with the centripetal acceleration using the formulas a(t) = r * α(t) and ac = r * ω^2.
Step-by-step explanation:
The rotational velocity of a motorized wheel at all subsequent times is given by the equation w(t) = c + bt, where c = 1.5564 and b = 6.97s^-2. To find the time at which the rotational acceleration is at a maximum, we can differentiate the equation for angular velocity with respect to time to find the equation for angular acceleration. Taking the derivative of w(t), we get a(t) = b. The maximum acceleration occurs when the constant b is the largest, which means the maximum acceleration occurs at all times. Therefore, the time at which the rotational acceleration is at a maximum is at any time after t = 0s.
To find the maximum tangential acceleration of a point on the wheel a distance r = 1.17m from its center, we can use the equation a(t) = r * α(t), where α(t) represents the angular acceleration. Since the angular acceleration is constant and equal to b = 6.97s^-2, the maximum tangential acceleration is given by a(t) = 1.17m * 6.97s^-2 = 8.1529 m/s^2.
The total acceleration of a point on the wheel can be found by combining the tangential acceleration with the centripetal acceleration. The centripetal acceleration ac is given by the equation ac = r * ω^2, where ω represents the angular velocity. At any time t, the angular velocity can be calculated using the equation ω(t) = w(t) - w0, where w(t) represents the angular velocity at time t and w0 represents the initial angular velocity. Substituting the given values, we can find the angular velocity at any time t. Then, using the formula ac = r * ω^2, we can calculate the centripetal acceleration. Finally, adding the tangential acceleration and the centripetal acceleration, we can find the total acceleration.