Skip to main content
Pearson+ LogoPearson+ Logo
Ch 09: Rotation of Rigid Bodies
Back
Previous problem
Next problem
All textbooksYoung & Freedman Calc 14th EditionCh 09: Rotation of Rigid BodiesProblem 9

Chapter 9, Problem 9

A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 4.00 kg, while the balls each have mass 0.300 kg and can be treated as point masses. Find the moment of inertia of this combination about an axis (b) perpendicular to the bar through one of the balls;

Verified Solution
Video duration:
3m
This video solution was recommended by our tutors as helpful for the problem above.
498
views
Was this helpful?

Video transcript

Hello everyone. So in this problem we have that two balls are attached to the ends of the unicorn bar. The mass of the two m long, four kg long bar is greater than that of the individual balls, which are point masses with masses of 40.0.3 kilograms each. We want to find the combinations moment of inertia about an axis passing between one of the balls and the bar that is perpendicular to. So in this apparatus we have are With two balls attached to each end. We want to find the moment of inertia where the axis of rotation is through one of these bars or balls. And we know that the mass of the long bar is equal to four kg at the length of the bar is equal to two m, which is much greater in the diameter. one of the balls, we also know the mass of each ball Is equal to .3 kg. Generally you recall that the moment of inertia is equal to the sum of the mass of each point. Project times the distance from the axis of rotation squared. Now, in this case we have a point object which is the ball which is a distance R is equal to The length of the bar two m. Now this wall where we are rotating about R is equal to zero. So we won't have to add this contribution to the moment of inertia. The total moment of inertia in this apparatus is equal to the moment of inertia of the bar plus the moment of inertia of one of the balls where we recall that the moment of inertia of the bar is just one third and elsewhere about the end of its axis. And the moment on our show at this point, object, which is the ball equal to M. R square R. Is the distance from the rotation of access. So in total we can make these substitution now where we distinguish that this M. Is the end of the bar and this M is When we make these substitutions, we get that I total is equal to one third times of the bar, which is four kg Times the length of the bar, which is two m squared Plus mass of one of the balls. 10.3 kg The distance of the ball to the rotation of access, which is two m squared. As we get on doing this calculation, I total is equal to 6.53 kg times meters squared, which is answer choice C. All this sounds great
Previous problemNext problem
Related Practice
Textbook Question
An airplane propeller is 2.08 m in length (from tip to tip) with mass 117 kg and is rotating at 2400 rpm (rev/min) about an axis through its center. You can model the propeller as a slender rod. (a) What is its rotational kinetic energy? (b) Suppose that, due to weight constraints, you had to reduce the propeller's mass to 75.0% of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in rpm?
1862
views
Textbook Question
You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cm long and has mass 0.400 kg. (b) One of your engineers has proposed to reduce the moment of inertia by bending the rod at its center into a V-shape, with a 60.0o angle at its vertex. What would be the moment of inertia of this bent rod about an axis perpendicular to the plane of the V at its vertex?
2057
views
1
comments
Textbook Question
A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 4.00 kg, while the balls each have mass 0.300 kg and can be treated as point masses. Find the moment of inertia of this combination about an axis (a) perpendicular to the bar through its center;
2306
views
2
rank
1
comments
Textbook Question
A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 4.00 kg, while the balls each have mass 0.300 kg and can be treated as point masses. Find the moment of inertia of this combination about an axis (c) parallel to the bar through both balls;
527
views
Textbook Question
A compound disk of outside diameter 140.0 cm is made up of a uniform solid disk of radius 50.0 cm and area density 3.00 g/cm^2 surrounded by a concentric ring of inner radius 50.0 cm, outer radius 70.0 cm, and area density 2.00 g^cm^2. Find the moment of inertia of this object about an axis perpendicular to the plane of the object and passing through its center.
886
views
Textbook Question
A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 4.00 kg, while the balls each have mass 0.300 kg and can be treated as point masses. Find the moment of inertia of this combination about an axis (d) parallel to the bar and 0.500 m from it.
682
views