Chapter 2: Problem 51

Give an example of a motion which is rotatory as well as periodic.

Short Answer

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Question: Provide an example of a motion that is both rotatory and periodic. Answer: A common example of a motion that is both rotatory and periodic is the rotation of the hands of a clock. The hands rotate around a fixed axis (the center), and they repeat their motion at regular time intervals, such as the second hand completing a full rotation every 60 seconds, the minute hand every 60 minutes, and the hour hand every 12 hours.

Step by step solution

Example of Rotatory and Periodic Motion

A common example of a motion that is both rotatory and periodic is the rotation of the hands of a clock. The hands rotate around a fixed axis (the center), and they repeat their motion at regular time intervals.

Description of the Motion

In the case of the hands of a clock, the motion can be broken down as follows: 1. The second hand of the clock completes a full rotation (360 degrees) every minute (60 seconds). This motion is rotatory as it goes around a fixed axis, and periodic as it takes exactly 60 seconds for the hand to complete a full rotation and return to its starting position. 2. The minute hand rotates at a slower speed, completing a full rotation in 60 minutes (3600 seconds). Like the second hand, this motion is also rotatory and periodic, as the hand rotates around the fixed axis and takes a regular interval of time to complete one full rotation. 3. The hour hand moves even slower than the minute hand, taking 12 hours (43200 seconds) to complete a full rotation. This is still a rotatory and periodic motion as it revolves around the fixed axis and repeats its motion at a regular interval. In all these cases, the motion of the clock hand is both rotatory (due to the rotation around the fixed axis) and periodic (due to the regular intervals of time for each hand to complete a full rotation).

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Key Concepts

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

Example of Rotatory Motion

Rotatory motion occurs when an object turns about an internal axis, effectively spinning in place. A classic illustration of this is a fan's blades as they circle their central point. Another quintessential exhibit is a merry-go-round, its seats spinning around its central pillar.

Delving deeper into this concept, let's consider the movement of Earth itself. The Earth rotates on its axis, resulting in day and night cycles, which is yet another instance of rotatory motion. This type of motion is characteristic because all parts of the object move through the same angle over the same time period, despite their varying distances from the axis.

Definition of Periodic Motion

Periodic motion is a motion that repeats itself at fixed time intervals, like the oscillation of a pendulum or the vibration of a guitar string. Importantly, this type of motion can be predictable and is described by its period—the length of time it takes for one cycle of motion to complete.

Think of the beating human heart as a biological metronome; its regular rhythm is a vital example of periodic motion within our bodies. These examples help us intuitively comprehend the hallmark of periodic motion: consistent repetition over identical time frames.

Rotation of Clock Hands

The movement of clock hands is an excellent representation of motion that's both rotatory and periodic. Starting with the second hand of a clock, which sweeps a full 360-degree rotation each minute, we see a recurring action tied to a regular period. The minute hand, though moving slowly, follows suit, completing its own loop every hour. Finally, the hour hand forms its large, slow circle, finishing one rotation every 12 hours.

With clock hands, not only do we encounter a case of motion around a fixed point, but we also observe the hands returning to their starting positions at consistent intervals. This dual nature makes the rotation of clock hands an emblematic example in physics, illustrating the concepts of both rotatory and periodic motions in a tangible, everyday context.

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Give an example of a motion which is rotatory as well as periodic.

Short Answer

Step by step solution

Example of Rotatory and Periodic Motion

Description of the Motion

Key Concepts

Example of Rotatory Motion

Definition of Periodic Motion

Rotation of Clock Hands

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