Lab 9

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Life Chiropractic College West *

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Physics

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Apr 3, 2024

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Lab 8: Centripetal Motion Purpose To use a ball orbiting in a radial gravitational field to study parts of centripetal motion. Baseball bats being swung, race cars turning a corner, the swing of your arm when you walk, the motion of satellites around the earth all have something in common, centripetal motion. What causes something to move in a circle though? In all those examples, there is some type of force pulling the object towards the center of rotation, whether it is a muscle, friction, or gravity, many different types of forces can lead to circular motion. Whatever caused the force aside, the speed that an object travels in circular motion can be measured in many different ways and is dependent on many variables. Centripetal, radian, radial, tangent, velocity The angular speed of an object moving in circular motion is the number of radians or degrees turned in a second. The linear speed or tangential speed describes something different. When an object is traveling in circular motion, the tangential speed is the speed of the object in the direction that is tangent to the circle. You can also measure the radial velocity, which is yet another way to measure the velocity of an object in centripetal motion. In this activity you will look at and compare the difference between tangential and rotational speeds. 1. Start Virtual Physics and select Centripetal Motion from the list of assignments. The lab will open in the Mechanics laboratory. 2. The laboratory will be set up with a ball on the 2D experimental window. There is a rocket attached to the ball. It is set to launch the ball into orbit around a radial gravity sink, which will pull the ball towards the center of the screen, just like a satellite being put into orbit around a planet. After the rocket turns off, the only force acting on the ball is gravity. When you click Force the rocket will fire for 1 second. You will record the position, velocity, and angular velocity of the ball.

3. Click Force to start the ball in motion and watch V r through a couple of orbits. Record your observations in Question 1. 4. Now watch the value of ω through a couple of orbits. Record your observations in Question 2. 5. Fill in the r , V r and ω values at the indicated points in the table below. You can click the red Pause button to stop the motion at any point and then restart it by clicking Start again. 6. Click the Total button in the top left corner of the control panel. Observe the total velocity for a full orbit and fill in the values in the table for the 4 orbit locations. Record your observations in Question 3. 7. Calculate the tangential velocity at the 4 points using the equation V t = r x ω . Answer Question 4. 1. What does V r measure? What does the sign of the value mean? How does the value change as the ball completes an orbit? What does Vr measure?: Vr measures how fast the object is moving either toward (negative) or away from (positive) the center of rotation. What does the sign of the value mean?: The sign of Vr tells you the direction of motion - positive for outward, negative for inward. How does the value change as the ball completes an orbit?: Vr changes from positive to negative and back as the ball goes around the center; it's highest when moving away, lowest when moving toward, and near zero at the extremes of its orbit. 2. What does ω measure? Where is the value largest? Why do you think it is largest at that point? 1. What does ω measure? : ω measures the angular velocity of the object in its circular motion. It tells you how quickly the object is rotating around the center of rotation. 2. Where is the value largest? : The value of ω is largest when the object is closest to the center of rotation during its orbit. 3. Why do you think it is largest at that point? : The angular velocity ω is largest when the object is closest to the center of rotation because, in circular motion, objects tend to move faster when they are closer to the center. This is due to the conservation of angular momentum, which causes the object to speed up as it moves closer to the center of rotation.

Location r (m) Radial Velocity (m/s) Angular Velocity (rad/s) Total Velocity (m/s) Tangential Velocity (m/s) Starting point 61.1317 0.0000 0.0000 0.0000 0.0000 1/4 of the way around 53.1436 -13.4247 0.0000 13.4247 13.4247 1/2 way around 41.8779 -23.4788 0.0000 23.4788 23.4788 3/4 of the way around 21.1888 -47.5419 0.0000 47.5419 47.5419 3. Where in the orbit is the total velocity greatest? How does the total velocity change through a full orbit? The total velocity is greatest at the point farthest from the center of rotation in the orbit. Throughout a full orbit, the total velocity follows a pattern: it's highest at the starting point, decreases as the object moves toward the center, reaches a minimum at the closest point to the center, and then increases again as the object moves away from the center. 4 . How does tangential velocity change throughout the orbit? What is the difference between the total velocity and tangential velocity? Tangential velocity changes throughout the orbit by varying in magnitude and direction. It starts at zero, increases to a maximum, decreases, and returns to zero during the orbit. Total velocity is the overall velocity in circular motion, taking into account both radial (inward) and tangential components. Tangential velocity is just the component responsible for the object's movement along the circular path, without any radial component. 6 . Calculate the period of the orbit. The period of an orbit is the time it takes for an object to complete one full revolution around the center of rotation. To calculate the period, you can use the provided data. First, identify the time it takes for the object to return to the "Starting point" in the data, which represents one full orbit. In this case, it takes approximately 30.014 seconds to complete the orbit. 7. Is the orbit perfectly circular? Is it stable or is the ball gradually spiraling into the center of gravity?

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