### Rotational Dynamics Problem**Problem Statement:**The 300-kg gear has a radius of gyration about its center of mass \( O \) of \( k_O = 400 \) mm. If the wheel is subjected to a couple moment of \( M = 300 \) N·m, determine its angular velocity 6 seconds after it starts from rest and no slipping occurs. Also determine the friction force that the ground applies to the wheel. Solve the problem using Impulse and Momentum.**Figure Explanation:**The provided diagram shows a gear placed on the ground subjected to a couple moment \( M = 300 \) N·m, which is causing it to rotate. The following key measurements and values are illustrated:- The moment \( M = 300 \) N·m is applied to the gear.- The radius of the gear is labeled as 0.6 meters.- The center of mass \( O \) is centered in the middle of the gear.- The radius of gyration \( k_O \) about its center of mass \( O \) is 400 mm (0.4 meters).**Objectives:**1. **Determine the Angular Velocity:** - We aim to calculate the angular velocity of the gear after 6 seconds from rest using the principles of impulse and momentum. - Given data and formula usage will be applied to find the angular velocity.2. **Determine the Friction Force:** - Assess the friction force that prevents slipping and calculate the magnitude of this force.### Solutions Approach:Using the principles of impulse and momentum for rotational systems, we will derive the angular velocity and the friction force. Here's an outline of the approach:#### Step 1: Convert Units- Radius of gyration \( k_O = 0.4 \) meters.#### Step 2: Calculate the Moment of Inertia- Use \( I_O = m \cdot k_O^2 \) where \( m = 300 \) kg.- \( I_O = 300 \cdot (0.4)^2 = 300 \cdot 0.16 = 48 \) kg·m\(^2\)#### Step 3: Apply Impulse and Momentum Principles- Calculate the angular impulse provided: \( M \cdot t = 300 \cdot 6 = 1800 \) N·m·s- Angular impulse is equal to

Given:The mass of the gear is .The radius of gyration is .The couple moment is .The radius is…

3. The 300-kg gear has a radius of gyration about its center of mass O of ko=400 mm. If the wheel is subjected to a couple moment of M= 300 N-m, determine its angular velocity 6 s after it starts from rest and no slipping occurs. Also determine the friction force that the ground applies to the wheel. Solve the problem using Impulse and Momentum. M 300 Nm 0.6 m

3. The 300-kg gear has a radius of gyration about its center of mass O of ko=400 mm. If the wheel is subjected to a couple moment of M= 300 N-m, determine its angular velocity 6 s after it starts from rest and no slipping occurs. Also determine the friction force that the ground applies to the wheel. Solve the problem using Impulse and Momentum. M 300 Nm 0.6 m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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