A 6.0 - m long rod has a mass of 1⁄3kg. Its moment of inertia from...

A 6.0 - m long rod has a mass of 1⁄3kg. Its moment of inertia from an axis at one of its end is (in kg. m2)

Expert Solution

If body is assume to be continuous, then one can use the technique of integration to obtain the moment of inertia of the body about given axis or line. The elements should be choosen that the perpendicular from different points of element to given line differ only infinitesimal amounts... Please comment if you have any doubts..

genius_generous answered 1 year ago

moment of inertia of a rod

Starting with the formula for the moment of inertia of a rod rotated around an axis through one end perpendicular to its length (I=M ℓ² / 3), prove that the moment of inertia of a rod rotated about an axis through its center perpendicular to its length is I=M ℓ² / 12. You will find the graphics in Figure 10.12 useful in visualizing these rotations.

The moment of inertia of a thin ring of mass M and radius R about its...

The moment of inertia of a thin ring of mass M and radius R about its symmetry axis is ICM = MR2 Kira is working the ring-toss booth at a local carnival. While waiting for customers, Kira occupies her time by twirling one of the plastic rings of mass M and radius R about her finger. Model the motion of the plastic ring as a thin ring rotating about a point on its circumference. What is the moment of inertia of...

Show that the moment of inertia of a spherical shell of radius R and mass M...

Show that the moment of inertia of a spherical shell of radius R and mass M about an axis through its centre is 2/3 MR2. Show also that the moment of inertia of a uniform solid sphere of radius R and mass M is 2/5MR2. The spheres are allowed to roll (from rest), without slipping a distance L down a plane inclined at a angle θ to the horizontal. Find expressions for the speeds of the spheres at the bottom...

Find the moment of inertia of a circular disk of radius R and mass M that...

Find the moment of inertia of a circular disk of radius R and mass M that rotates on an axis passing through its center. [Answer: ½ MR2] Step 1: Pictorial representation: Sketch a neat picture to represent the situation. Step 2: Physical representation: 1) Cut the disk into many small rings as it has the circular symmetry. 2) Set up your coordinate system and choose its origin at the pivot point (or the axle location) for convenience. Then choose a...

String is wrapped around an object of mass M = 0.3 kg and moment of inertia...

String is wrapped around an object of mass M = 0.3 kg and moment of inertia I = 0.01 kgÂ·m2. You pull the string with your hand straight up with some constant force F such that the center of the object does not move up or down, but the object spins faster and faster (see the figure). This is like a yo-yo; nothing but the vertical string touches the object. When your hand is a height y0 = 0.26 m...

A hollow ball has mass M=2.0kg, radius R=0.35m, and moment of inertia about the center of...

A hollow ball has mass M=2.0kg, radius R=0.35m, and moment of inertia about the center of mass I=(2/3)MR2. The ball is thrown without bouncing, to the right with an initial speed 2.0m/s and backspin. The hoop moves across the rough floor (coefficient of sliding friction = 0.25) and returns to its original position with a speed of 0.5 m/s. All surfaces and the hoop may be treated as ideally rigid. Develop an expression for angular velocity of the hoop as...

3. A rigid uniform disk (moment of inertia I = 1/2 m R2) has a mass...

3. A rigid uniform disk (moment of inertia I = 1/2 m R2) has a mass m = 10 Kg and radius R = 2 m, it is free to rotate around a fixed axis passing through its center and is at rest at t = 0 s. A constant force F = 20 N is applied halfway between the center and the edge of the disk, in a direction perpendicular to the disk radius. (i) Calculate the torque, the...

Two balls connected by a rod as shown in the figure below (Ignore rod’s mass). What is the moment of inertia of the system?

Two balls connected by a rod as shown in the figure below (Ignore rod’s mass). What is the moment of inertia of the system? Given : mX = 400 grams = 0.4kg mY = 500 grams = 0.5 kg rX = 0cm = 0m rY = 30cm = 0.3m

The Mass Moment of Inertia of a body is a property that measures the resistance of...

The Mass Moment of Inertia of a body is a property that measures the resistance of the body to angular acceleration True False The Parallel-Axis Theorem is I = IG + md2 True False The resultant (summation) moment about the mass center due to all the external forces is equal to the moment of inertia about center of mass times the angular velocity of the body. True False Mathematically, three equations with four unknowns cannot be solved. True False The...

Find the mass, the center of mass, and the moment of inertia about the z-axis for...

Find the mass, the center of mass, and the moment of inertia about the z-axis for the hemisphere x^2+y^2+z^2=1, z >(greater than or equal to) 0 if density is sqrt(x^2+y^2+z^2)

Question