/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 For an object moving in a circle... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

For an object moving in a circle, which of the following quantities are zero over one revolution: (a) displacement, (b) average velocity, (c) average acceleration, (d) instantaneous velocity, and (e) instantaneous centripetal acceleration?

Short Answer

Expert verified
Displacement and average velocity are zero over one revolution in a circular motion but average acceleration, instantaneous velocity, and instantaneous centripetal acceleration are not.

Step by step solution

01

Analyze Item (a)

The displacement is the change in position of an object. In circular motion, over one complete revolution, the object returns to its starting position. Thus, the overall change in position is zero. Therefore, the displacement over one revolution is zero.
02

Analyze Item (b)

The average velocity is the total displacement divided by the total time. We already determined that over one revolution, the displacement is zero, thus, the average velocity is also zero.
03

Analyze Item (c)

The average acceleration is defined as the change in velocity divided by the time it takes for the change. In a circular motion, the direction of the velocity of an object changes all the time (even though the speed may remain constant). Hence, there is a non-zero average acceleration.
04

Analyze Item (d)

The instantaneous velocity at any point in time is the velocity of the object at that precise moment. In a circular motion, at all times the particle is in motion, and hence there is always some non-zero instantaneous velocity.
05

Analyze Item (e)

Instantaneous centripetal acceleration is the acceleration at any given point along the circular path. Even if an object moves at a constant speed, there is acceleration towards the center of the circle. So the instantaneous centripetal acceleration is never zero for an object in circular motion.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Displacement in Circular Motion
Displacement refers to the change in position of an object. In circular motion, displacement over a full circle, or one complete revolution, is intriguing. Imagine drawing a circle and starting at one point. If you trace around the circle and end up back at the starting point, your journey's displacement is zero. This is because displacement only considers the initial and final points — it ignores the path taken to get there. Hence, for any object that completes a full circle, the overall displacement is zero.
Average Velocity in Circular Motion
Average velocity in circular motion can be a bit misleading due to the nature of motion. Average velocity is calculated as the total displacement divided by the total time taken. In the context of one complete circle, since the displacement is zero, the average velocity must also be zero. It’s essential to distinguish this from speed; velocity has a directional component, and when tracking in a full circle, that overall direction, and hence the average velocity, is zero.
Centripetal Acceleration
Centripetal acceleration is a fundamental concept in understanding circular motion. It refers to the acceleration directed towards the center of the circle that keeps an object moving in its curved path. This acceleration ensures the object doesn't flit off in a straight line by constantly changing the object's direction. Even if an object maintains a constant speed, the direction change results in centripetal acceleration. This acceleration is never zero when an object is in uniform circular motion.
Instantaneous Velocity
Instantaneous velocity is the measure of an object's velocity at a specific moment in time. In circular motion, an object is always moving, which means it always has velocity. This velocity is tangent to the circle's path. Regardless of the position on the path, the object will have a non-zero instantaneous velocity. This is different from average velocity as it focuses on one particular instant rather than the entire motion across a round path.
Physics Education
Physics education, especially in high school or introductory college courses, is crucial for understanding fundamental concepts like circular motion. These foundational ideas are vital as they not only help in academic pursuits but also in recognizing their occurrence in daily life. For example, understanding how centripetal acceleration keeps your vehicle on curved roads can enhance safe driving practices. Moreover, learning to analyze concepts such as displacement and velocity helps sharpen analytical skills useful in various fields and everyday problem-solving scenarios. Physics provides a framework that describes how things work, and circular motion is just one part of this fascinating puzzle.

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Most popular questions from this chapter

At the Fermi National Accelerator Laboratory (Fermilab), a large particle accelerator, protons are made to travel in a circular orbit \(6.3 \mathrm{~km}\) in circumference at a speed of nearly \(3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}\). What is the centripetal acceleration on one of the protons?

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