Question

A motorized wheel is spinning with a rotational velocity of 0=1.17 rad/s. At =0 s, the operator switches the wheel to a higher speed setting. The rotational velocity of the wheel at all subsequent times is given by ()=0arctan(c+2) where c=1.5574 and =6.53 s−2. At what time max is the rotational acceleration at a maximum?

What is the maximum tangential acceleration at of a point on the wheel a distance =1.21 mR=1.21 m from its center?

Answer 1

The maximum rotational acceleration can be found by taking the derivative of the angular velocity function and finding its maximum. Calculus would be necessary for an accurate answer. The tangential acceleration at the point on the wheel can then be calculated using the distance to that point and the angular acceleration.

Step-by-step explanation:

To determine the time tmax when the rotational acceleration is at a maximum, we need to consider the derivative of the angular velocity ω(τ) given by ω(τ) = ω0arctan(c+2τ). The maximum rotational acceleration occurs when the derivative of ω(τ) with respect to time is at its maximum. However, since the exact time isn't provided in the question, and the derivation is complex, we typically need to use calculus to find the precise value of tmax. From there, the maximum tangential acceleration at can be found using the relation at = rα, where r is the distance from the center of the wheel and α is the angular acceleration.