3.0 m/s 2 3.4 m/s 2 4.3 m/s 2 3.8 m/s 2 2.7 m/s 2 A wheel (radius = 12 cm) is mo
ID: 2020522 • Letter: 3
Question
3.0 m/s2
3.4 m/s2
4.3 m/s2
3.8 m/s2
2.7 m/s2
A wheel (radius = 12 cm) is mounted on a frictionless, horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel. A light cord wrapped around the wheel supports a 0.40-kg object. If released from rest with the string taut, the object is observed to fall with a downward acceleration of 3.0 m/s2. What is the moment of inertia (of the wheel) about the given axIS? (DIAGRAM PLEASE!!)
0.023 kg × m2 0.013 kg × m2 0.020 kg × m2 0.016 kg × m2 0.035 kg × m2Explanation / Answer
radius of the wheel r = 0.25 m moment inertia of the axis I = 0.040 kg m2 mass of the wheel m = 0.50 kg ............................................................................... According to Newton second law the hanging weight m*g-T=m*a where T is the tension in the cord T = m*g-m*a ........ (1) Apply Newton second law to t the wheel T*R=I*a/R ....... (2) solving 1 and 2 we have a = [mg / ( m+I/r)] a = [0.50kg *9.8 m/sec2 / 0.50 kg + ( 0.040 kg m2 / 0.25 m)] = 4.30 m/s^2 NOTE: post second as separate.
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