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A gear radius 0.4m and a gear radius 1.2m are connected by a belt If the smaller gear is rotating with an angular velocity of 10rads what is the angular velocity of the larger gear?
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∙ 14y ago
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If A gear of radius 0.4 m and a gear of radius 1.2 m are connected by a belt as in the following figure if the smaller gear is rotating with an angular velocity of 10rad find the angular velocity?
# We usually use belts to connect PULLEYS; Chains to connect SPROCKETS. Gears have teeth and usually directly mesh together without belts. However, there are gear-like pulleys that have teeth on them but require belts that also have teeth. Possibly what your thinking of... but the math problem is the same with or without a belt. # The key is to recognize the ratio between the pulleys (or sprockets or gears.) 1.2m / 0.4m = 3 ... so the ratio is 3:1 # If the smaller pulley (gear) is the drive, then the driven (bigger) one will turn 1/3 times for each turn of the small one, for a ratio of 3:1. If the big pulley (gear) is the drive, then the driven (smaller) one would turn 3 times for each single turn of the big one. # You did not state the time of rotation. (per second? per minute?) Regardless, the the big pulley (gear) will have 1/3 (one third) the angular velocity of the small pulley (gear.) So (ANSWER) your BIG pulley (or gear) will have angular velocity of 3.333333... (three and one third) radians per time unit.
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