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Question: An athlete whirls a 7.46 kg hammer tied to the end of a 1.4 m chain in a simple horizontal circle where you should ignore any vertical deviations. The hammer moves at the rate of 0.297 rev/s. What is the centripetal acceleration of the hammer? Assume his arm length is included in the length given for the chain. Answer in units of m/s 2 .
The formula for centripetal acceleration is a = rw^2. Here, r refers to the radius of the circle and w refers to the angular velocity. In your problem: - The radius (r) is 1.4 m. - The angular velocity (w) is 0.297 rev/s. But we need to convert revolutions per second into radians per second because the units of our radius were in meters. There are 2? radians in one revolution, so w = 0.297rev/s * 2? rad/rev = 1.86 rad/s. Substituting these values into our formula, we get: a = r*w^2 a = 1.4 m *(1.86 rad/s)^2 This will give you the centripetal acceleration in m/s^2. To calculate this, square the angular velocity (1.86^2 = 3.46), then multiply that result by the radius (1.4*3.46), which will give you a centripetal acceleration of approximately 4.84 m/s^2.
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