The linear speed is v = 4√3 t. The tangential acceleration is a_t = dv/dt = d(4√3 t)/dt = 4√3 m/s². At t = 1 s, v = 4√3 m/s. The radial acceleration is a_r = v²/r = (4√3)² / 4 = (163) / 4 = 48/4 = 12 m/s². The radial direction +r̂ points towards the center. The total acceleration vector is the sum of a_t (tangential) and a_r (radial, inward). The angle φ between the resultant acceleration and the radial direction (+r̂, pointing inward) satisfies tan(φ) = a_t / a_r.
A particle moves in a circle of radius 4 m. Its linear speed is given by 4√3 t, where t is the time measured in seconds. At t = 1 s, the angle made by the resultant acceleration - r̂ with direction (+ r̂ is the radial direction) is given by φ. Which one among the following is the correct value of φ ?
Asked in UPSC Geoscientist 2024 · Topic: Mechanics (Newton's Laws of Motion and their applications)
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