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The second hand and the minute hand on one type of clock are the same length. Find the ratio $\left(a_{\mathrm{c}, \mathrm{second}} / a_{\mathrm{c}, \text { minuted }}\right)$ of the centripetal accelerations of the tips of the second hand the minute hand.

3600

Physics 101 Mechanics

Chapter 5

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

Simon Fraser University

Lectures

03:28

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.

03:43

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.

02:14

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00:30

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02:09

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04:21

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in this problem, you have to five the ratio between the regular acceleration of the second hand of the clock and the angular acceleration with minute hand on the clock. Now, we're not really given any information apart from the fact that they're the same length. But we actually do know some other crucial information that will help us solve this problem. The period of a second hand is 60 seconds, right? That's the amount of time that it takes for it to go. Once around the clock, counting off a minute, the period for a minute hand is gonna be 60 times 60. That's the number of seconds in an hour. That's 3600 seconds. Now we know that the equation for angular acceleration is V squared over r. But we don't know a velocity. But now that we have the periods, that's easy to Seoul for. We know that t is two pi r over V, and so we can rearrange to sell for tea and have it in terms of quantity. Is that we either no or going to cancel out? Let's start with the second hand books. Um, angular acceleration. So did not it with Alfa Second. That's gonna be two pi r squared over t squared times r squared. So that's just be squared over r But now in terms of tea and that's gonna give us, um, a final answer of four pi squared are over. Key s squared. Now, when we do the same thing for a minute hand, we're gonna have exactly the same equation as we get up there. Just this time, it's going to be in terms of the period of the minute hand, Tien and we're told the radius of the same. So I'm not going to note them any differently. All right, so now let's figure out our fraction We've f s over Alfa M. Yeah, that's equal to a four pi squared are over. T s squared all over. Four pi squared are over t m squared. Now, as you can see, everything is gonna cancel out except our two periods. And that's gonna give us t m squared over t s squared. Now from there we can plug in. We said that our minute hand period was 3600 seconds squared on our second period was 60 seconds squared. We do it that math, we find that the relationship between the two is 3000 and 600 that's gonna be the answer to her question. The relation between the angular acceleration.

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