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Force and Acceleration on a Turntable - Part I

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Here's an activity in which you'll examine static friction as a cause of circular motion. For our equipment, we'll be using a motor which has a metal disc attached to it. As I turn on the motor, it will rotate up to some maximum speed. I'm going to turn it off now, and place a penny on the disc. Now if I turn the motor on, you would expect the penny to move in a circular path for a while, but at some point the disc will start to move fast enough that the penny will slide off. Let's take a look at that. What determines how fast a disc has to be rotating before the penny slides off? Let's define some quantities first. The penny, which has mass m, is located a distance R from the center of the turntable. When the disc starts rotating, the penny starts moving with velocity V which is tangent to the circular path. Newton's first law, the normal tendency of any object is to move in a straight line unless a net external force acts on the object. The force acting on the penny to make it move in a circle is static friction between the penny and the disc. This force points to the center of the circle. The net horizontal force acting on the penny when it's moving at constant speed is just the static friction pointing to the center. By Newton's second law, the net force is the product of the mass and acceleration of the penny. The acceleration is a centripetal acceleration; it points to the center of the circular path and has a magnitude equal to the square of the penny's speed, divided by the radius of the path. As the disc speeds up, the penny's centripetal acceleration increases a greater net force is required to keep the penny moving in a circle. Static friction increases to provide that force. The static friction cannot increase without limit. The limit is determined by the weight of the penny and the coefficient of static friction between the penny and the disc. When the limit is reached and exceeded, the friction force can no longer hold the penny on a circular path. This is when the penny slides. Actually, we detect this as the disc sliding out from under the penny. Now here's a problem for you to do. Suppose I take three pennies, place them at different distances from the center. When I turn the motor on, in what order will the pennies slide off? Or will they all slide off at the same time? The key to answering the question is to consider, or to rank the pennies, according to the amount of centripetal force required to hold them in circular motion at a radius R at a given frequency. Write down your answer, and then submit it with your explanation. After you've submitted it you'll receive a link to a video clip to see what actually happens.

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