This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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1. Spherical bobs are preferred in simple pendulum experiments because their symmetrical shape minimizes air resistance, ensuring that air drag has a negligible effect on the pendulum's motion. Additionally, the center of mass of a spherical bob is precisely at its geometric center, which simplifies calculations and provides more accurate measurements of the pendulum's length and period. 2. A simple pendulum in simple harmonic motion: Diagram: ` O (pivot) | | L (length of string) | | | A <--- B (equilibrium) ---> C (max displacement) (max displacement) ` (A simple diagram showing a pivot, a string of length L, and a bob swinging between two extreme positions A and C, passing through an equilibrium position B.) a) The maximum velocity* of the bob occurs at the equilibrium position (B), which is the lowest point of its swing. b) The maximum acceleration* of the bob occurs at the extreme positions (A and C), where the displacement from equilibrium is greatest. 3. Step 1: Convert the final angular velocity from revolutions per minute to radians per second. _f = 60 revmin × 2 rad1 rev × 1 min60 s _f = 2 rads Step 2: Use the kinematic equation for angular motion to find the angular acceleration. Given: _0 = 0 rad/s (from rest), _f = 2 rad/s, t = 4 s. _f = _0 + t 2 rads = 0 rads + (4 s) = 2 rads4 s = ()/(2) rads^2 ≈ 1.57 rads^2 The angular acceleration is ()/(2) rads^2 or 1.57 rads^2 4. Step 1: Convert the radius to meters. r = 40 cm = 0.40 m Step 2: Calculate the total angular displacement in radians. The stone makes 10 complete revolutions. Each revolution is 2 radians. = 10 rev × 2 radrev = 20 rad Step 3: Calculate the angular velocity. = ( )/(t) = 20 rad3.8 s ≈ 16.53 rads Step 4: Calculate the linear velocity. v = r v = (0.40 m) × ( (20)/(3.8) rads ) v = (8)/(3.8) ms v ≈ 6.59 ms The angular velocity is (20)/(3.8) rads or 16.53 rads and the linear velocity is (8)/(3.8) ms or 6.59 ms