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1. Make a drawing of the path of an object in circular motion at constant speed. On that path, use a dot to represent the object's position at time t1. Label this point as O, and draw a vector at O to represent the magnitude and direction of the object's velocity at time t. Draw another dot to represent the object's position at a later time t2, shortly after t1, and label this point P. Draw a vector at P to show the magnitude and direction of the object's velocity at time t2. 2. Redraw the velocity vectors with the tail of one vector (point P) at the tail of the other vector (point O). Keep the same size and direction as in the previous drawing. To find the acceleration of the object, you are interested in the change in velocity (Av). The change Av is the increment that must be added to the velocity at time t so that the resultant velocity has the new direction after the elapsed time At = ti – t2. Add the change in velocity Av to your drawing of the velocity vectors; it should be a straight line connecting the heads of the vectors. 3. On your drawing from question 1, label the distancer from the center of the circle to points O and P. In the limit that the time interval is very small, the arc length distance traveled by the object can be approximated as a straight line. Use this approximation to label the distance traveled by the object along the circle from point O to P in terms of the object's velocity and the elapsed time.

1. Make a drawing of the path of an object in circular motion at constant speed. On that path, use a dot to represent the object's position at time t1. Label this point as O, and draw a vector at O to represent the magnitude and direction of the object's velocity at time t. Draw another dot to represent the object's position at a later time t2, shortly after t1, and label this point P. Draw a vector at P to show the magnitude and direction of the object's velocity at time t2. 2. Redraw the velocity vectors with the tail of one vector (point P) at the tail of the other vector (point O). Keep the same size and direction as in the previous drawing. To find the acceleration of the object, you are interested in the change in velocity (Av). The change Av is the increment that must be added to the velocity at time t so that the resultant velocity has the new direction after the elapsed time At = ti – t2. Add the change in velocity Av to your drawing of the velocity vectors; it should be a straight line connecting the heads of the vectors. 3. On your drawing from question 1, label the distancer from the center of the circle to points O and P. In the limit that the time interval is very small, the arc length distance traveled by the object can be approximated as a straight line. Use this approximation to label the distance traveled by the object along the circle from point O to P in terms of the object's velocity and the elapsed time.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Please answer questions 1-6 in the first image based off the picture in image 2.
Circular Motion and Acceleration x + com/courses/219263/assignments/1685970?module_item_id=5554714 s 3 Translate Dashboard A My Drive - Google. A Section 6 - A.2281 = ZOOM E Rapid Writing A Arch 4561 Case Stu... and then exporting the result as a PDF. Warm up 1. Make a drawing of the path of an object in circular motion at constant speed. On that path, use a dot to represent the object's position at time t1. Label this point as O, and draw a vector at O to represent the magnitude and direction of the object's velocity at time t1. Draw another dot to represent the object's position at a later time t2, shortly after t1, and label this point P. Draw a vector at P to show the magnitude and direction of the object's velocity at time t2. 2. Redraw the velocity vectors with the tail of one vector (point P) at the tail of the other vector (point O). Keep the same size and direction as in the previous drawing. To find the acceleration of the object, you are interested in the change in velocity (Av). The change Av is the increment that must be added to the velocity at time tį so that the resultant velocity has the new direction after the elapsed time At = t1 – t2. Add the change in velocity Av to your drawing of the velocity vectors; it should be a straight line connecting the heads of the vectors. 3. On your drawing from question 1, label the distance r from the center of the circle to points O and P. In the limit that the time interval is very small, the arc length distance traveled by the object can be approximated as a straight line. Use this approximation to label the distance traveled by the object along the circle from point O to P in terms of the object's velocity and the elapsed time. 4. The triangle drawn in question 2 (with v and Av) is similar to the triangle drawn in question 3 (with r and the straight line distance traveled by the object) because they have the same apex angle. Use the relationship of similar triangles to write an equation that connects the sides and the bases of the two triangles. 5. Solve your equation for Av/At to get an expression for the acceleration in terms of the object's uniform velocity and the distance r. 6. From your equation, is the acceleration of an object in circular motion ever zero? Does the magnitude of the acceleration change with time? Prediction Does an object moving in a circle accelerate? If so, does the magnitude of the acceleration change with time? Explain your reasoning. Use the acceleration equation you derived in the Warm-up to support your claim. • Previous Next 立
Transcribed Image Text:Circular Motion and Acceleration x + com/courses/219263/assignments/1685970?module_item_id=5554714 s 3 Translate Dashboard A My Drive - Google. A Section 6 - A.2281 = ZOOM E Rapid Writing A Arch 4561 Case Stu... and then exporting the result as a PDF. Warm up 1. Make a drawing of the path of an object in circular motion at constant speed. On that path, use a dot to represent the object's position at time t1. Label this point as O, and draw a vector at O to represent the magnitude and direction of the object's velocity at time t1. Draw another dot to represent the object's position at a later time t2, shortly after t1, and label this point P. Draw a vector at P to show the magnitude and direction of the object's velocity at time t2. 2. Redraw the velocity vectors with the tail of one vector (point P) at the tail of the other vector (point O). Keep the same size and direction as in the previous drawing. To find the acceleration of the object, you are interested in the change in velocity (Av). The change Av is the increment that must be added to the velocity at time tį so that the resultant velocity has the new direction after the elapsed time At = t1 – t2. Add the change in velocity Av to your drawing of the velocity vectors; it should be a straight line connecting the heads of the vectors. 3. On your drawing from question 1, label the distance r from the center of the circle to points O and P. In the limit that the time interval is very small, the arc length distance traveled by the object can be approximated as a straight line. Use this approximation to label the distance traveled by the object along the circle from point O to P in terms of the object's velocity and the elapsed time. 4. The triangle drawn in question 2 (with v and Av) is similar to the triangle drawn in question 3 (with r and the straight line distance traveled by the object) because they have the same apex angle. Use the relationship of similar triangles to write an equation that connects the sides and the bases of the two triangles. 5. Solve your equation for Av/At to get an expression for the acceleration in terms of the object's uniform velocity and the distance r. 6. From your equation, is the acceleration of an object in circular motion ever zero? Does the magnitude of the acceleration change with time? Prediction Does an object moving in a circle accelerate? If so, does the magnitude of the acceleration change with time? Explain your reasoning. Use the acceleration equation you derived in the Warm-up to support your claim. • Previous Next 立
hinks that the person has a constant acceleration when moving at a constant speed. Yet a thirc speeu is ating, so there of change of their velocity, not their speed. Since each component of the person's velocity cha me. You decide to settle the issue by making a model of the ride and measuring the magnitude c when it spins at a constant speed. EQUIPMENT wood base with a bearing post, a skateboard wheel and ruler. You can mark a spot on the skateb ruler onto the wheel as shown below. Tape the ruler on top of the spool if you make a longer plat NON-SHATTER hapter 3 Sections 3.8 (derivation), and Chapter 6 Section 6.1 to 6.2.
Transcribed Image Text:hinks that the person has a constant acceleration when moving at a constant speed. Yet a thirc speeu is ating, so there of change of their velocity, not their speed. Since each component of the person's velocity cha me. You decide to settle the issue by making a model of the ride and measuring the magnitude c when it spins at a constant speed. EQUIPMENT wood base with a bearing post, a skateboard wheel and ruler. You can mark a spot on the skateb ruler onto the wheel as shown below. Tape the ruler on top of the spool if you make a longer plat NON-SHATTER hapter 3 Sections 3.8 (derivation), and Chapter 6 Section 6.1 to 6.2.
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