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
CR££D, let's knock this out. Given: Mass m = 2 kg Diameter D = 34 cm Initial angular speed _0 = 3.5 rad/s Final angular speed _f = 0 rad/s (comes to rest) Number of revolutions N = 3 First, convert the diameter to radius in meters and calculate the total angular displacement: Radius R = (D)/(2) = 34 cm2 = 17 cm = 0.17 m Angular displacement = N × 2 rad = 3 × 2 = 6 rad (iii) Moment of inertia of the turn table about its axis. Step 1: Use the formula for the moment of inertia of a solid disk. For a solid disk rotating about its central axis, the moment of inertia I is given by: I = (1)/(2) m R^2 Step 2: Substitute the given mass and calculated radius. I = (1)/(2) (2 kg) (0.17 m)^2 Step 3: Calculate the moment of inertia. I = (1 kg) (0.0289 m^2) I = 0.0289 kg · m^2 The moment of inertia is 0.0289 kg·m^2. (i) Angular momentum Step 1: Use the formula for angular momentum. Angular momentum L is given by L = I . Since the question refers to an initial speed, we calculate the initial angular momentum L_0. L_0 = I _0 Step 2: Substitute the calculated moment of inertia and initial angular speed. L_0 = (0.0289 kg · m^2) (3.5 rad/s) Step 3: Calculate the initial angular momentum. L_0 = 0.10115 kg · m^2/s The initial angular momentum is 0.101 kg·m^2/s. (ii) The time taken for it to come to rest after it is switched off. Step 1: Calculate the angular acceleration () using rotational kinematics. We use the equation: _f^2