Why circular motion includes continuous

The predictive ability of an equation becomes more complicated when one of the quantities included in the equation is raised to a power. For instance, consider the following equation relating the net force F net to the speed v of an object moving in uniform circular motion. This equation shows that the net force required for an object to move in a circle is directly proportional to the square of the speed of the object. For a constant mass and radius, the F net is proportional to the speed 2.

The factor by which the net force is altered is the square of the factor by which the speed is altered. Subsequently, if the speed of the object is doubled, the net force required for that object's circular motion is quadrupled.

And if the speed of the object is halved decreased by a factor of 2 , the net force required is decreased by a factor of 4. The mathematical equations presented above for the motion of objects in circles can be used to solve circular motion problems in which an unknown quantity must be determined. The process of solving a circular motion problem is much like any other problem in physics class. The process involves a careful reading of the problem, the identification of the known and required information in variable form, the selection of the relevant equation s , substitution of known values into the equation, and finally algebraic manipulation of the equation to determine the answer.

Consider the application of this process to the following two circular motion problems. Determine the acceleration and the net force acting upon the car. The solution of this problem begins with the identification of the known and requested information. The solution is as follows:. The solution is as follows. A kg halfback makes a turn on the football field.

The halfback sweeps out a path that is a portion of a circle with a radius of meters. The halfback makes a quarter of a turn around the circle in 2. Determine the speed, acceleration and net force acting upon the halfback. In Lesson 2 of this unit, circular motion principles and the above mathematical equations will be combined to explain and analyze a variety of real-world motion scenarios including amusement park rides and circular-type motions in athletics. Anna Litical is practicing a centripetal force demonstration at home.

She fills a bucket with water, ties it to a strong rope, and spins it in a circle. Anna spins the bucket when it is half-full of water and when it is quarter-full of water. In which case is more force required to spin the bucket in a circle? Explain using an equation as a "guide to thinking.

It will require more force to accelerate a full bucket of water compared to a half-full bucket. So the greater the mass, the greater the force. A Lincoln Continental and a Yugo are making a turn. The Lincoln is four times more massive than the Yugo. If they make the turn at the same speed, then how do the centripetal forces acting upon the two cars compare.

The centripetal force on the Continental is four times greater than that of a Yugo. So 4 times the mass means 4 times the force. The Cajun Cliffhanger at Great America is a ride in which occupants line the perimeter of a cylinder and spin in a circle at a high rate of turning. When the cylinder begins spinning very rapidly, the floor is removed from under the riders' feet.

What affect does a doubling in speed have upon the centripetal force? Doubling the speed of the ride will cause the force to be four times greater than the original force. So 2X the speed means 4X the force that's from 2 2. Determine the centripetal force acting upon a kg child who makes 10 revolutions around the Cliffhanger in The direction of a centripetal force is toward the center of rotation, the same as for centripetal acceleration.

Both forms of the equation depend on mass, velocity, and the radius of the circular path. You may use whichever expression for centripetal force is more convenient. By definition, the centripetal force is directed towards the center of rotation, so the object will also accelerate towards the center. A straight line drawn from the circular path to the center of the circle will always be perpendicular to the tangential velocity.

Note that, if you solve the first expression for r , you get. From this expression, we see that, for a given mass and velocity, a large centripetal force causes a small radius of curvature—that is, a tight curve. This video explains why a centripetal force creates centripetal acceleration and uniform circular motion.

It also covers the difference between speed and velocity and shows examples of uniform circular motion. Some students might be confused between centripetal force and centrifugal force. Centrifugal force is not a real force but the result of an accelerating reference frame, such as a turning car or the spinning Earth. Centrifugal force refers to a fictional center fleeing force. In this activity, you will measure the swing of a golf club or tennis racket to estimate the centripetal acceleration of the end of the club or racket.

You may choose to do this in slow motion. The swing of the golf club or racket can be made very close to uniform circular motion.

For this, the person would have to move it at a constant speed, without bending their arm. The length of the arm plus the length of the club or racket is the radius of curvature. Accuracy of measurements of angular velocity and angular acceleration will depend on resolution of the timer used and human observational error. A car follows a curve of radius m at a speed of Compare the centripetal acceleration for this fairly gentle curve taken at highway speed with acceleration due to gravity g.

The image above shows the forces acting on the car while rounding the curve. In this diagram, the car is traveling into the page as shown and is turning to the left. Friction acts toward the left, accelerating the car toward the center of the curve. Because friction is the only horizontal force acting on the car, it provides all of the centripetal force in this case. Therefore, the force of friction is the centripetal force in this situation and points toward the center of the curve.

Calculate the centripetal acceleration of an object following a path with a radius of a curvature of 0. Identify two examples of forces that can cause centripetal acceleration. Use the Check Your Understanding questions to assess whether students master the learning objectives of this section. If students are struggling with a specific objective, the formative assessment will help identify which objective is causing the problem and direct students to the relevant content. As an Amazon Associate we earn from qualifying purchases.

Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4. Changes were made to the original material, including updates to art, structure, and other content updates. Skip to Content Go to accessibility page. Physics 6. My highlights. Table of contents. Chapter Review. Test Prep.

By the end of this section, you will be able to do the following: Describe centripetal acceleration and relate it to linear acceleration Describe centripetal force and relate it to linear force Solve problems involving centripetal acceleration and centripetal force.

Teacher Support The learning objectives in this section will help your students master the following standards: 4 Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to: C analyze and describe accelerated motion in two dimensions using equations, including projectile and circular examples. D calculate the effect of forces on objects, including the law of inertia, the relationship between force and acceleration, and the nature of force pairs between objects.

In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Circular and Rotational Motion, as well as the following standards: 4 Science concepts. Teacher Support Consider Figure 6. Ladybug Motion in 2D In this simulation, you experiment with the position, velocity, and acceleration of a ladybug in circular and elliptical motion. Click to view content.

Teacher Support [BL] [OL] [AL] Using the same demonstration as before, ask students to predict the relationships between the quantities of angular velocity, centripetal acceleration, mass, centripetal force.

Centripetal force is perpendicular to tangential velocity and causes uniform circular motion. The larger the centripetal force F c , the smaller is the radius of curvature r and the sharper is the curve. Centripetal Force and Acceleration Intuition This video explains why a centripetal force creates centripetal acceleration and uniform circular motion.

Teacher Support Some students might be confused between centripetal force and centrifugal force. Imagine that you are swinging a yoyo in a vertical clockwise circle in front of you, perpendicular to the direction you are facing.

If the string breaks just as the yoyo reaches its bottommost position, nearest the floor.