Centripetal Force

Today you are going to study an object that moves in a circle. Today you are going to study an object that moves in a circle. An object that moves in circular motion must have a force acting on it that is directed toward the center of the circle. An object that moves in circular motion must have a force acting on it that is directed toward the center of the circle. This could be something as simple as a string pulling a ball into circular motion. This could be something as simple as a string pulling a ball into circular motion.

The string is pulling on the ball. The string is pulling on the ball. Strings cannot push. Strings cannot push. The circular motion could be a road forcing a car to turn a curve. The circular motion could be a road forcing a car to turn a curve.

The road continually pushes toward the center of the curve. The road continually pushes toward the center of the curve.

Even in a vertical loop amusement park ride, when a car is at the top of the loop, the track is actually pushing it downward toward the center of the circle in which it is travelling at that moment. in which it is travelling at that moment.

Forces that make objects move in circular motion are called Forces that make objects move in circular motion are called centripetal forces. Centripetal means “center-seeking.” Centripetal means “center-seeking.” This force should not be confused with the psuedo force commonly known as centrifugal. This force should not be confused with the psuedo force commonly known as centrifugal. Centrifugal means “center-fleeing,” and Centrifugal means “center-fleeing,” and centrifugal forces are not real.

Today you will measure the centripetal force in a particular circular motion and Today you will measure the centripetal force in a particular circular motion and show that it satisfies Newton’s Second Law:.

The apparatus you will use is shown below. Spring Masses Bob Pulley Slotted String Index Radius

When viewed from above the hand-turned apparatus looks like this

The acceleration in this circular motion is one associated with a change in the direction of the velocity vector, not the length of the velocity vector. The acceleration in this circular motion is one associated with a change in the direction of the velocity vector, not the length of the velocity vector. It, just like the centripetal force, also points toward the center of the circle. It, just like the centripetal force, also points toward the center of the circle. To calculate the acceleration you have to determine the angular velocity. To calculate the acceleration you have to determine the angular velocity.

Angular velocity is an angle measurement divided by time. Angular velocity is an angle measurement divided by time. For example if you make one full spin in 2 seconds of time, then your angular velocity would be divided by 2 seconds which reduces to /s. For example if you make one full spin in 2 seconds of time, then your angular velocity would be divided by 2 seconds which reduces to /s. Many of you have heard about 33 and a 1/3 rpm phonographic records that your parents or grandparents had when they were young. The rpm stands for revolutions per minute, and it is an angular velocity measurement. Many of you have heard about 33 and a 1/3 rpm phonographic records that your parents or grandparents had when they were young. The rpm stands for revolutions per minute, and it is an angular velocity measurement.

In lab today you will determine an angular velocity based on an angular measurement of radians instead of degrees. In lab today you will determine an angular velocity based on an angular measurement of radians instead of degrees.

One radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. 1 rev = = 2  radians (rad) segments gets to here. 2  segments gets completely around.

To get the angular velocity measured in terms of rad/s, you will make the following measurements. To get the angular velocity measured in terms of rad/s, you will make the following measurements. Count the number (N) of cycles the apparatus makes, and measure the time (T) to make these N turns. Count the number (N) of cycles the apparatus makes, and measure the time (T) to make these N turns. Repeat until you have three different time measurements involving N turns each time. Repeat until you have three different time measurements involving N turns each time. Take the average of the three T ’s. Take the average of the three T ’s.

Divide this average T by N to get the average time (  ) for one rotation. In other words Divide this average T by N to get the average time (  ) for one rotation. In other words   = T/N Then the angular velocity (  ) is Then the angular velocity (  ) is  = 2   ..

Though it is not shown here, it is not difficult to show that the centripetal acceleration (a) is given by Though it is not shown here, it is not difficult to show that the centripetal acceleration (a) is given by a =  2 R where R is the radius of the circle. where R is the radius of the circle.

Once you have a, you will multiply it by the mass of the swinging object (the bob). (The value will be on the blackboard.) Once you have a, you will multiply it by the mass of the swinging object (the bob). (The value will be on the blackboard.) You will then compare this force to the force necessary to position the bob at a distance R from its rotation axis when the apparatus is not spinning. You will then compare this force to the force necessary to position the bob at a distance R from its rotation axis when the apparatus is not spinning. Spring Masses Bob Pulley Slotted String Index Radius For your lab exam, you must know this method of determining the centripetal force.