Rotational_Mechanics

# Rotational_Mechanics - Circular Motion Circular motion is...

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Circular Motion Circular motion is done about a line we call an axis . There are two types of this motion: Rotation : when an object spins about an axis that passes through it. Example: The Earth rotates once about its polar axis each day. Revolution : when an object moves about an external axis. Example: The Earth revolves once about the sun each year. Other Examples? 1

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Speeds involved in Circular Motion Linear speed : Distance covered per unit time by a point on the object in motion. Units: meters per second (m/s), or miles per hour (mph). Symbol used is: v (same as usual) Rotational speed (or Angular speed) : Amount of angle swept out per unit time. Units: radians per second (1 /s or s - 1 ), or revolutions per minute (rpm). Symbol used is: ω (the small Greek letter ”omega”) 2
Some Questions 1. Linear speed is often called tangential speed . Why? 2. When a wheel rolls, is the rotational speed the same for every point on the wheel? 3. When a wheel rolls, is the linear speed the same for every point on the wheel? Linear Speed ( v ) is directly proportional to: radial distance from axis of rotation ( r ) rotational speed ( ω ) If rotational speed is expressed in radians per second then: v = r × ω 3

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Do Now When a wheel rolls, it covers a distance equal to its circumference with every revo- lution. A wheel has a circumference of 1 meter. A larger wheel has a circumference of 2 meters. Each wheel has a rotational speed of 4 rev- olutions per minute (rpm). How far (in meters) will the large wheel go in 1 minute? How far (in meters) will the smaller wheel go in 1 minute? 4
Suppose you get a ﬂat tire while driving. You put on the ”toy spare” tire that came with the car. The toy spare tire is smaller in diameter than your other tires. How does this afect your driving? 5

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What causes Circular Motion? Suppose we swing an object tied to a rope around in uniform circular motion. (”Uniform” means angular speed ( ω ) is constant.) Does a point on the object move with constant linear speed? Does a point on the object move with constant velocity? Does a point on the object accelerate? In what direction? Does a point on the object feel a force? In what direction? How does the object move if we cut the rope? 6
To keep an object in circular motion, we must constantly exert a force on the object that is perpendicular to the object’s velocity at all times and directed inward toward the center of the circular motion. This force is called centripetal force . Example Cause of the centripetal force Ball swinging on a string String pulls ball inward. Electrons orbiting Nucleus Nucleus attracts Electrons.

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Rotational_Mechanics - Circular Motion Circular motion is...

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