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.
ScanSolve AI Answer
Here are the solutions to Question 3.2: Given: Moment of inertia, I = 7.5 kg · m^2 Mass, m = 18 kg Rotational speed, N = 3000 r/min 3.2.1 The kinetic energy of the wheel Step 1: Convert the rotational speed to angular velocity in radians per second. = N × 2 rad1 rev × 1 min60 s = 3000 r/min × (2)/(60) rad/s = 100 rad/s ≈ 314.159 rad/s Step 2: Calculate the rotational kinetic energy (KE_rot). The formula for rotational kinetic energy is: KE_rot = (1)/(2)I^2 KE_rot = (1)/(2)(7.5 kg · m^2)(100 rad/s)^2 KE_rot = (1)/(2)(7.5)(10000^2) J KE_rot = 37500^2 J KE_rot ≈ 37500 × (3.14159)^2 J KE_rot ≈ 37500 × 9.8696 J KE_rot ≈ 369990 J KE_rot ≈ 370 kJ The kinetic energy of the wheel is 370 kJ. 3.2.2 The radius of gyration of the wheel in cm Step 3: Calculate the radius of gyration (k). The moment of inertia is also given by I = mk^2. We can rearrange this to solve for k: k = sqrt((I)/(m)) k = sqrt(7.5 kg) · m^218 kg k = sqrt(0.41666... m)^2 k ≈ 0.6455 m Step 4: Convert the radius of gyration from meters to centimeters. k = 0.6455 m × 100 cm1 m k ≈ 64.55 cm The radius of gyration of the wheel is 64.55 cm. Drop the next question.