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Feb 24, 2024 · Just a few examples are the tension in the rope on a tether ball, the force of Earth’s gravity on the Moon, friction between roller skates and a rink floor, a banked roadway’s force on a car, and forces on the tube of a spinning centrifuge. Any net force causing uniform circular motion is called a centripetal force.
Take a look at the curve to the right. No matter what value the x variable takes on the curve, the y variable stays the same. This is a classic example of a relationship called independence. Two quantities are independent if one has no effect on the other. The curve is a horizontal, straight line represented by the general form equation… y = k
Sep 9, 2023 · Concave and convex describe the shape of a curve. Remember that “concave” resembles a cave! The terms “concave” and “convex” describe the curvature of objects or mathematical functions. They’re ubiquitous in a range of disciplines, including optics, mathematics, engineering, and everyday life.
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Let's begin by graphing some examples of motion at a constant velocity. Three different curves are included on the graph to the right, each with an initial displacement of zero. Note first that the graphs are all straight. (Any kind of line drawn on a graph is called a curve. Even a straight line is called a curve in mathematics.) This is to be exp...
Compare the displacement-time equation for constant velocity with the classic slope-intercept equation taught in introductory algebra.
Although our hypothetical object has no single velocity, it still does have an average velocity and a continuous collection of instantaneous velocities. The average velocity of any object can be found by dividing the total displacement by the total time.
Instantaneous velocity is the limit of average velocity as the time interval shrinks to zero. As the endpoints of the line of average velocity get closer together, they become a better indicator of the actual velocity. When the two points coincide, the line is tangent to the curve. This limit process is represented in the animation to the right.
Since a curved line has no single slope we must decide what we mean when asked for the acceleration of an object. These descriptions follow directly from the definitions of average and instantaneous acceleration. If the average acceleration is desired, draw a line connecting the endpoints of the curve and calculate its slope. If the instantaneous a...
You should also notice that the slope was negative from 3.0 s to 6.5 s. During this time the speed was decreasing. This is not true in general, however. Speed decreases whenever the curve returns to the origin. Above the horizontal axis this would be a negative slope, but below it this would be a positive slope. About the only thing one can say abo...
In kinematics, there are three quantities: displacement, velocity, and acceleration. Given a graph of any of these quantities, it is always possible in principle to determine the other two. Acceleration is the time rate of change of velocity, so that can be found from the slope of a tangent to the curve on a velocity-time graph. But how could displ...
If you trip and fall on your way to school, your acceleration towards the ground is greater than you'd experience in all but a few high performance cars with the \"pedal to the metal\". Acceleration and velocity are different quantities. Going fast does not imply accelerating quickly. The two quantities are independent of one another. A large accel...
There are more things one can say about acceleration-time graphs, but they are trivial for the most part.
Example Problem For Curvilinear Motion. A slotted link is rotating about fixed pivot O with a counterclockwise angular velocity of 3 rad/s, and a clockwise angular acceleration of 2 rad/s 2. The movement of the link is causing a rod to slide along the curved channel, as shown.
Banked Curves. towards the centre of the curve (not parallel with the bank!) In other words, Fn sin θ is the centripetal force directed .
People also ask
What if a graph was curved?
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What happens if a curve on a velocity-time graph is straight?
How do you graph motion at a constant velocity?
The graph of displacement versus time in Figure \(\PageIndex{3a}\) is a curve rather than a straight line. The slope of the curve becomes steeper as time progresses, showing that the velocity is increasing over time.
