The moment of inertia for an extended body is I = r² dm. Prove that for a circular disc of mass M and radius R the moment of inertia, about an axis through its centre, is I = MR². A 80-kg man stands still on the rim of an initially stationary circular carousel of radius 3 m and mass 200 kg. The man begins to walk at 1 ms-¹ (with respect to the ground) along the rim. What is his angular velocity, w? What is his angular momentum? What is the angular velocity of the carousel? How fast is the man walking with respect to the carousel?

The moment of inertia for an extended body is I = r² dm. Prove that for a circular disc of mass M and radius R the moment of inertia, about an axis through its centre, is I = MR². A 80-kg man stands still on the rim of an initially stationary circular carousel of radius 3 m and mass 200 kg. The man begins to walk at 1 ms-¹ (with respect to the ground) along the rim. What is his angular velocity, w? What is his angular momentum? What is the angular velocity of the carousel? How fast is the man walking with respect to the carousel?

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

See similar textbooks

Related questions

Q: The moment of inertia of the pulley about its axis is I = 0.005 kg.m?. If the 5-kg mass A is…

Q: The 52-kg reel has a radius of gyration about its center O of ko = 240 mm. If it is released from…

Q: In the system shown, the mass at A is 10 kg and that at B is 5 kg. The mass-moment of inertia of the…

Q: moment c Angular velocity

Q: A disk, mass 2kg, radius 0.5m spins at a constant angular speed w = 12s¹ about an axle that is at an…

Q: This disk has a radius of 2.7 meter and a mass of 80 kg. What is the mass moment of inertia about an…

A: The mass of disc is The radius of disc is

Q: A 5-kg quarter of a circular disk with a radius of 500 mm and a radius of gyration kç = 0.25 m is…

A: Given Data The radius of the quarter circle, r=0.500m The radius of gyration, KG=0.25m. The mass of…

Q: 2 An object is made of two identical uniform 3m long rods connected as shown. The total mass of the…

Q: A composite pendulum is made of a uniform slender rod and a uniform disk. If the rod has length of…

A: Find the mass moment of inertia about axis x' that pass through point O.

Q: Consider a disk of radius R = 0.2 m, mass of mg = 20 kg, and moment of inertia of IG= 0.40 kg-m²…

A: Given:To find:(a) Magnitude of tension T.(b) Velocity of the cylinder after 3 seconds.

Q: The two small spheres of mass m each are connected by the light rigid rod which lies in the plane.…

A: Given: m = 2.3 kg L = 375 mm

Q: The drum shown in Fig. (a) has a radius of gyration of 30 cm and weights 1,8 kN. It is supported by…

A: Given data: k=30 cmw=1.8 kJW=1 kNr=37.5 cm Need to determine the angular acceleration of the drum.

Q: m A hollow wheel of mass given by m = 50 kg rolls down an incline of 30° without slipping. The inner…

A: Given-Information:To-Determine:a. Moment of inertia.b. Linear acceleration of the wheel's center of…

Q: At the instant shown, the uniform slender rod with mass m = 33 kg is pin-supported at point O. It…

Q: The object consists of an 8 lb thin bar welded to a 12 lb disk. It is released from rest at…

A: The weight of disc is The weight of bar is The radius of disc is The length of bar is

Q: A stepped cylinder has the dimensions R₁ = 0.30 m, R₂ = 0.65 m, and the radius of gyration, k, is…

A: The inner radius is .The outer radius is .The radius of gyration of cylinder is .The mass of…

Q: The 154-kg wheel has a radius of gyration about its center O of ko = 280 mm, and radius r = 0.4 m.…

Q: Determine the In secon

A: Given data is

Q: Determine the mass moment of inertia for the following rigid bodies about an axis at its center…

Q: 4. The composite body shown below is formed by a combination of a thin rod and a thin, circular dis…

A: Given,

Q: At the instant shown, the uniform slender rod with mass m = 32 kg is pin-supported at point O. It…

Q: The sphere with mass m = 40 kg rolls down the inclined plane of angle = 33 without slipping.…

Q: The uniform rod of length 4b and mass m is bent into the shape shown. The diameter of the rod is…

Q: a satellite's orientation can be controleld using a flywheel placed inside the satellite and fixed…

A: Moment of inertia of flywheel I2 = mR22 =…

Q: The moment of inertia of a planet revolving around a star is treated like a point mass. Using the…

Q: The pendulum consists of a 7-pound slender rod and an 11-pound plate with even negligible thickness.…

Q: The 24-kg uniform thin hollow square plate is pinned at point O, and its side L = 0.3 m. Determine…

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

The moment of inertia for an extended body is I = [r² dm. Prove that for a circular disc of
mass M and radius R the moment of inertia, about an axis through its centre, is I = MR².
A 80-kg man stands still on the rim of an initially stationary circular carousel of radius 3 m and
mass 200 kg. The man begins to walk at 1 ms-1 (with respect to the ground) along the rim.
What is his angular velocity, w? What is his angular momentum?
What is the angular velocity of the carousel? How fast is the man walking with respect to the
carousel?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: The inertia of the disc

VIEW

Step 3: the carousel problem:

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

The 150-kg wheel shown in Fig. In the initial position shown, the velocity of Gis 2 m/s down the plane, and the spring is stretched 150 mm. If the spring modulus is 1000 N/m, what will be the maximum stretch of the spring? has a radius of gyration of 360 mm with respect to its center of mass G. www 150 kg 30°
The 10-kg door shown is 80 cm by 120 cm and has a constant thickness before the circular cut (diameter = 15 cm) is made. Calculate the centroid and mass moment of inertia about the z-axis (through the origin) of the door with the hole cut. $15cm gy ૧º- ↓ 80cm 120cm
A pendulum consists of a 4 kg rod and an 8 kg cylinder. (a) Determine the loca- tion of the CG of the pendulum. (b) Calculate the mass moment of inertia of the pendulum about an axis perpendicular to the page and passing through the CG. y 2.5 m G 0.5 m
The uniform rod of length 4b and mass m is bent into the shape shown. The diameter of the rod is small compared with its length. Determine the moments of inertia of the rod about the three coordinate axes. Use the values m = 7.9 kg and b = 485 mm. Answers: 1xxx = i lyy= i Izz = i kg.m² kg-m² kg-m²