Centripetal force

\( \newcommand\) • • Learning Objectives By the end of this section, you will be able to: • Calculate coefficient of friction on a car tire. • Calculate ideal speed and angle of a car on a turn. Any force or combination of forces can cause a centripetal or radial acceleration. 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. The direction of a centripetal force is toward the center of curvature, the same as the direction of centripetal acceleration. According to Newton’s second law of motion, net force is mass times acceleration: net \(F = ma \). For uniform circular motion, the acceleration is the centripetal acceleration - \(a = a_c\). Thus, the magnitude of centripetal force \(F_c\) is \[ F_c = ma_c.\] By using the expressions for centripetal acceleration \(a_c\) from \( a_c = \frac\):The frictional force supplies the centripetal force and is numerically equal to it. Centripetal force is perpendicular to velocity and causes uniform circular motion. The larger the \(F_c\), the smaller the radius of curvature \(r\) and the sharper the curve. The second curve has the same \(v\), but a larger \(F_c\) produces a smaller \(r'\). Example \(\PageIndex = 1125 \, N. \nonumber\] Strategy for (b) Figure shows the forc...

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Equipment • Platform with String • This is the platform on which the cup will sit while being spun in circles • Over time, the knots in the string will slip, and the platform will no longer be level. This can be fixed by untying and releveling the platform. Since this is quite tedious, the TA or instructor should be informed as soon as the platform seems to be slipping so that it can be repaired without a time constraint. • Cup for water • Any transparent cup will work, but a cheap plastic one is ideal because the cup will eventually be launched across the room on accident. • Water • Be sure to locate a source of water before starting your presentations. • If you think you might spill water, you can practice with the tennis ball in the cup instead of water. • A brave/ well practiced demonstrator • This demo is scary at first, but with practice can become second nature. In simplest terms, the water cup is undergoing uniform circular motion. Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle as well. An object moving in a circle is accelerating. Accelerating objects are objects that are changing their velocity; either the speed or the direction. ...

Recent Examples on the Web Lagrange points are stable areas of space where the gravitational pull of two large masses equals the centripetal force needed for a small object to keep pace, which means much less fuel is needed to stay in position. — Darren Orf, Popular Mechanics, 10 Feb. 2023 So, if the telescope moved into a higher orbit (a larger circular radius), the centripetal force would decrease. — Rhett Allain, Wired, 7 Jan. 2022 In this case, scientists installed a poll in the middle of the room to serve as an anchor for some serious centripetal force. — Carl Engelking, Discover Magazine, 8 May 2015 The basic concept of a O’Neill cylinder is that a spinning tube-like structure simulates gravity via a centripetal force acting on humans living on the cylinder’s inner surface. — Darren Orf, Popular Mechanics, 30 Jan. 2023 Objects traveling in a circular path experience an acceleration inward towards the center of the circle and a force—the centripetal force—outward from the center. — Kyle Hill, Discover Magazine, 10 Dec. 2013 The whole experiment takes on the look of a Gravitron ride as quadcopters whip around the pole at speeds exceeding 30 miles per hour, generating centripetal force 14 times the pull gravity. — Carl Engelking, Discover Magazine, 8 May 2015 This spun up the larger star, and the centripetal force flung off material in a huge disk well over a light years across. — Phil Plait, Discover Magazine, 12 Aug. 2011 The evidence suggests that there are centripet...

Learning Objectives By the end of the section, you will be able to: • Explain the equation for centripetal acceleration • Apply Newton’s second law to develop the equation for centripetal force • Use circular motion concepts in solving problems involving Newton’s laws of motion In centripetal acceleration, is given by the formula [latex][/latex] is [latex][/latex] in terms of mass, velocity, angular velocity, and radius of curvature: [latex][/latex] is perpendicular to the velocity and points to the center of curvature. Note that if you solve the first expression for r, you get Figure 6.20 The frictional force supplies the centripetal force and is numerically equal to it. Centripetal force is perpendicular to velocity and causes uniform circular motion. The larger the [latex][/latex] produces a smaller r′. Example What Coefficient of Friction Do Cars Need on a Flat Curve? (a) Calculate the centripetal force exerted on a 900.0-kg car that negotiates a 500.0-m radius curve at 25.00 m/s. (b) Assuming an unbanked curve, find the minimum static coefficient of friction between the tires and the road, static friction being the reason that keeps the car from slipping ( Figure 6.21 This car on level ground is moving away and turning to the left. The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. A minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway. Figure 6.2...

Any force or combination of forces can cause a centripetal or radial acceleration. 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. The direction of a centripetal force is toward the center of curvature, the same as the direction of centripetal acceleration. According to Newton’s second law of motion, net force is mass times acceleration: net F = ma F = ma size 12 is 6.23 By using the expressions for centripetal acceleration a c a c size 12 in terms of mass, velocity, angular velocity, and radius of curvature: 6.24 You may use whichever expression for centripetal force is more convenient. Centripetal force F c F c size 12, you get Figure 6.11 The frictional force supplies the centripetal force and is numerically equal to it. Centripetal force is perpendicular to velocity and causes uniform circular motion. The larger the F c F c size 12. What Coefficient of Friction Do Car Tires Need on a Flat Curve? (a) Calculate the centripetal force exerted on a 900 kg car that negotiates a 500 m radius curve at 25.0 m/s. (b) Assuming an unbanked curve, find the minimum static coefficient of friction, between the tires and the road, static friction being the reason that keeps the car from slipping (see Strategy and Solutio...