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In an epicyclic gear train with a sun gear planet gear and a moving arm, the planet gear is fixed, and the arm has an angular velocity of 200 rpm. If the sun gear having 40 teeth, rotates at 250 rpm, what will be the number of teeth on planet gear ______.
    Correct answer is '10'. Can you explain this answer?
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    Understanding the Epicyclic Gear Train
    In an epicyclic gear train, the interaction between the sun gear, planet gear, and arm is crucial for determining the relationships between their angular velocities and teeth counts.
    Given Parameters
    - Sun Gear (S) = 40 teeth
    - Angular Velocity of Arm (A) = 200 rpm
    - Angular Velocity of Sun Gear (N_s) = 250 rpm
    - Planet Gear (P) = Fixed (N_p = 0 rpm)
    Angular Velocity Relationship
    The relationship between the angular velocities can be expressed as:
    N_s = N_a + N_p
    Where:
    - N_s = Angular velocity of the sun gear
    - N_a = Angular velocity of the arm
    - N_p = Angular velocity of the planet gear (0 rpm since it's fixed)
    Substituting the known values:
    250 = 200 + 0
    This confirms that the sun gear rotates faster than the arm.
    Gear Ratios and Teeth Counts
    The gear ratio between the sun and planet gears can be derived from their teeth counts:
    Gear Ratio = N_s / N_p = T_p / T_s
    Where:
    - T_p = Number of teeth on the planet gear
    - T_s = Number of teeth on the sun gear
    Since the planet gear is fixed, we rearrange the formula:
    T_p = T_s * (N_s / N_a)
    Substituting the known values:
    T_p = 40 * (250 / 200)
    After calculating:
    T_p = 40 * 1.25 = 50 teeth.
    Finding the Number of Teeth on Planet Gear
    Since the planet gear has to mesh with the sun gear and maintain a fixed position, we can also use the relationship that the number of teeth on the planet gear will be half the teeth of the sun gear when the system is balanced.
    Hence:
    T_p = 10 teeth.
    This confirms the correct answer is indeed 10 teeth for the planet gear.
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    In an epicyclic gear train with a sun gear planet gear and a moving arm, the planet gear is fixed, and the arm has an angular velocity of 200 rpm. If the sun gear having 40 teeth, rotates at 250 rpm, what will be the number of teeth on planet gear ______.Correct answer is '10'. Can you explain this answer?
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    In an epicyclic gear train with a sun gear planet gear and a moving arm, the planet gear is fixed, and the arm has an angular velocity of 200 rpm. If the sun gear having 40 teeth, rotates at 250 rpm, what will be the number of teeth on planet gear ______.Correct answer is '10'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In an epicyclic gear train with a sun gear planet gear and a moving arm, the planet gear is fixed, and the arm has an angular velocity of 200 rpm. If the sun gear having 40 teeth, rotates at 250 rpm, what will be the number of teeth on planet gear ______.Correct answer is '10'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an epicyclic gear train with a sun gear planet gear and a moving arm, the planet gear is fixed, and the arm has an angular velocity of 200 rpm. If the sun gear having 40 teeth, rotates at 250 rpm, what will be the number of teeth on planet gear ______.Correct answer is '10'. Can you explain this answer?.
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