Virtual Labs

Which of the following best defines a simple pendulum?

a: A rigid body swinging about a fixed axis Explanation

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b: A point mass suspended from a fixed point by a massless string Explanation

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c: A rigid rod swinging about its center of mass Explanation

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d: A solid sphere rotating about its center Explanation

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What is the formula for the period (T) of a simple pendulum for small angles?

a: T=2π√(L/g) Explanation

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b: T=2π L/g Explanation

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c: T=2π√(g/L) Explanation

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d: T=2π/g Explanation

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The mass moment of inertia for a simple pendulum is given by which of the following formulas?

a: I=mL^2 Explanation

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b: I=1/2 mL^2 Explanation

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c: I=mL Explanation

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d: I=1/12 mL^2 Explanation

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What does the parallel axis theorem allow you to calculate?

a: The center of mass of a pendulum Explanation

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b: The moment of inertia about any axis parallel to the center of mass axis Explanation

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c: The angular frequency of oscillations Explanation

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d: The velocity of the pendulum bob at equilibrium Explanation

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Which of the following is true for a compound pendulum?

a: It has a massless string and a point mass Explanation

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b: The period is independent of the mass distribution Explanation

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c: The mass is distributed along its length Explanation

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d: It only follows simple harmonic motion for large angles Explanation

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Which of the following best illustrates a real-world application of the moment of inertia in pendulum systems?

a: Determining the stability of a bridge under dynamic load Explanation

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b: Designing clock pendulums for accurate timekeeping Explanation

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c: Calculating air resistance on a falling object Explanation

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d: Measuring temperature changes in a swinging pendulum Explanation

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When designing a playground swing or a pendulum-based amusement ride, why must engineers consider the moment of inertia?

a: To reduce air resistance during motion Explanation

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b: To control the smoothness and safety of oscillations Explanation

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c: To increase the mass of the system for stability Explanation

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d: To minimize the effect of gravity on the system Explanation

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Mass Moment Inertia of Pendulum