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Circular Motion Notes Circular Motion Notes Uniform circular motion is the motion of an object in a circle at a constant speed. • As an object moves in a circle, it is constantly changing its direction. • In all instances, the object is moving tangent to the circle. * constantly accelerating a = vΔ and v = Δ dΔ t t so a change in direction OR a change in speed will result in acceleration Circular Motion Notes Rotation: object is turning around an internal axis Revolution: object is moving around an external axis Finding Radians: As a general rule, when doing these calculations you should NOT leave any answers in terms of π! (Multiply it out!) A full circle has exactly 2π radians. To calculate radians, multiply the degrees by π/180. (Example: 120° = 2π/3 radians) Circular Motion Notes 150 degrees = ____________ radians? 150 degrees x π = 2.62 radians = 2.62 rad 180 3.14 ≠ π You are expected to use the (pi) buttonπ on your calculator for all of these problems! 1 revolution = 1 full turn of the circle 1) 310° = ? radians 2) 7 radians = ? degrees 3) A bicycle tire travels 4.5 revolutions. a) How many radians is this? b) How many degrees did it roll? Circular Motion Notes Linear (tangential) Velocity In one full rotation, the wheel has turned th e distance of the circumference. Position on the circular path will determine the linear velocity of an object. Linear velocity is calculated by multiplying the angular velocity by the radius: v = ω x radius B Two objects A and B are located on a spinning disk. Object A sits at a radius of 2 meters from the center, while object B sits 4 meters from the ω A center. If the angular speed for the disk ( ) is 200 rad/s, what are the linear speeds for objects A and B, respectively? Circular Motion Notes Angular vs. Linear Velocity Linear velocity = tangential velocity Every point on a rotating body has the same angular velocity even though every point does not have the same linear velocity. This is what makes angular velocity a useful measure of the rate of rotation. The blade of a lawn mower is rotating at an angular speed of 17 rev/s. The tangential speed of the outer edge of the blade is 32 m/s. What is the radius of the blade? Circular Motion Notes Centripetal Motion The word "centripetal" means "center- seeking." Since the acceleration for circular motion points toward the center of the circle, we call it centripetal acceleration. The force for circular motion is called centripetal force since it is toward the center of the circle. Centripetal Force The mass of the object times the square of its velocity, divided by the radius of the orbit or rotation. The force toward the center may be caused by gravity, friction, or another force. Circular Motion Notes Centripetal force holds an object in a circular path. Three properties govern the amount of centripetal force on an object: 1. The smaller the mass, the smaller the centripetal force needed. Fc Fc 2. The smaller the velocity of the object, the less centripetal force needed. v v Fc Fc Smaller Fc needed to Larger Fc is needed to force the object into orbit. counteract the greater velocity (v). Circular Motion Notes 3. The smaller the radius of the path, the more centripetal force you will have to apply. Fc Fc More force is Less force is needed here needed A 45 kg child riding a Ferris wheel has a tangential speed of 8.5 m/s. Find the magnitude of the centripetal force on the child if the distance from the child to the axis of the wheel is 18 m. Circular Motion Notes Circular Motion The blue object is moving with uniform circular motion around the red center. The object has a velocity that is tangent to the circular path. The object has an acceleration toward the center, called centripetal acceleration. Centripetal Acceleration Centripetal acceleration accelerates 2 the object toward the center of the a = v circular path c r 2 ac = centripetal acceleration (m/s ) v = velocity (m/s) r = radius of the circle (m) Attachments UniformCircularMotion.gif.
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