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The blade of a windshield wiper moves through an angle of 90.0 in 0.40 s. The tip of the blade moves on the arc of a circle that has a radius of 0.45 m. What is the magnitude of the centripetal acceleration of the tip of the blade?
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Physics 101 Mechanics
Dynamics of Uniform Circular Motion
Newton's Laws of Motion
Applying Newton's Laws
Rutgers, The State University of New Jersey
University of Michigan - Ann Arbor
Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows:
In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.
In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.
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this problem. We have to find the angular acceleration off the tip of a windshield wiper were given the number of degrees and it moves through the time that it takes, um, and the radius that it traverses. So we're gonna start out with our equations for velocity and our equations for the period now, the loss of what we want to find in orderto later solved for the angular acceleration. But we need the period to do this so that the period for any circular motion is given by two pi over Omega. And since Omega sequel to V Over R, This can be written in terms of V, which is what we want. But we have to be careful here because he describes the amount of time that it takes for an object to complete one full revolution in a circular path. However, we are only going across 90 degrees, as you can see right here. And so since 90 degrees represent 1/4 of a circle, this whole quantity is going to be multiplied by 1/4 now from their weaken, rewrite our equation for V and that is going to give us two pi R over tea times one foot. However, we already know the numerical value of tea were given in the problem that it takes near 0.4 seconds for the winter. Like Richard, reverse those 90 degrees. So all that's left for us to do know is wrecked our equation for angular acceleration and pulling it angular acceleration is equal to V squared over our and so now we can go ahead and we can plug in our equation that we got from T for V, which is going to give us that Alfa is equal to hi squared r over four. He squared after we simplify now a plug in our values. We know that our is equal to 0.45 meters, that she's given the problem statement and T is equal to 0.4 seconds. Also in the problem statement, we put this into her calculator. We get a value of 6.9 39 meters per second squared and those units check out signals of the units for angular acceleration. Rick around that 6.9 meters per second squared our final result
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