---### Physics Problem: Rotational Motion of a Turntable**Problem Statement:**3. A large wooden turntable has the shape of a flat uniform disk of radius 1.8 m and a total mass of 150 kg. The turntable is initially rotating at 4.00 rad/s about a vertical axis through its center. Suddenly, a 60 kg parachutist makes a soft landing near the outer edge.1. **(a)** Find the angular speed of the turntable after the parachutist lands. (Assume you can treat the parachutist as a particle.)2. **(b)** Compute the kinetic energy before and after the parachutist lands.**Detailed Explanation:**To solve this problem, we will use the principles of conservation of angular momentum and kinetic energy.#### (a) Angular Speed After Landing1. **Calculate Initial Angular Momentum (L_initial)** - For a disk, the moment of inertia (I) is \( I = \frac{1}{2} m r^2 \), where \( m \) is the mass and \( r \) is the radius. - For the turntable: \( I_{turntable} = \frac{1}{2} \times 150 \text{ kg} \times (1.8 \text{ m})^2 \) - Calculate \( I_{turntable} \): \[ I_{turntable} = \frac{1}{2} \times 150 \times 3.24 = 243 \text{ kg} \cdot \text{m}^2 \] - Initial angular momentum \( L_{initial} \) is given by \( L = I \omega \): \[ L_{initial} = 243 \times 4.00 = 972 \text{ kg} \cdot \text{m}^2 \cdot \text{s}^{-1} \]2. **Calculate Final Angular Momentum (L_final)** - After the parachutist lands, the system's moment of inertia changes. Treat the parachutist as a point mass at the edge of the disk. The moment of inertia of the parachutist is \( I_{parachutist} = m r^2 \): \[ I_{parachutist} = 60 \text{ kg} \

radius of disk (r) = 1.8 m mass (m) = 150 kg initial angular velocity = 4 rad/sec mass of…

3. A large wooden turntable has the shape of a flat uniform disk of radius 1.8 m and a total mass of 150 kg. The turntable is initially rotating at 4.00 rad/s about a vertical axis through its center. Suddenly, a 60 kg parachutist makes a soft landing near the outer edge. (a) Find the angular speed of the turntable after the parachutist lands. (Assume you can treat the parachutist as a particle.) (b) Compute the kinetic energy before and after the parachutist lands.

3. A large wooden turntable has the shape of a flat uniform disk of radius 1.8 m and a total mass of 150 kg. The turntable is initially rotating at 4.00 rad/s about a vertical axis through its center. Suddenly, a 60 kg parachutist makes a soft landing near the outer edge. (a) Find the angular speed of the turntable after the parachutist lands. (Assume you can treat the parachutist as a particle.) (b) Compute the kinetic energy before and after the parachutist lands.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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