If, for example, the father kept pushing perpendicularly for 2.00 s, he would give the merry-go-round an angular velocity of 13.3 rad/s when it is empty but only 8.89 rad/s when the child is on it. The angular accelerations found are quite large, partly due to the fact that friction was considered to be negligible. The angular acceleration is less when the child is on the merry-go-round than when the merry-go-round is empty, as expected. To develop the precise relationship among force, mass, radius, and angular acceleration, consider what happens if we exert a force\boldsymbol. If you push on a spoke closer to the axle, the angular acceleration will be smaller. The more massive the wheel, the smaller the angular acceleration. The greater the force, the greater the angular acceleration produced. Force is required to spin the bike wheel. There are, in fact, precise rotational analogs to both force and mass. These relationships should seem very similar to the familiar relationships among force, mass, and acceleration embodied in Newton’s second law of motion. The first example implies that the farther the force is applied from the pivot, the greater the angular acceleration another implication is that angular acceleration is inversely proportional to mass. Furthermore, we know that the more massive the door, the more slowly it opens. For example, we know that a door opens slowly if we push too close to its hinges. In fact, your intuition is reliable in predicting many of the factors that are involved. If you have ever spun a bike wheel or pushed a merry-go-round, you know that force is needed to change angular velocity as seen in Figure 1.
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