= (b) The figure below shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.0000 m and (total) mass M 100.0 mg. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point O. (a) What is the rotational inertia of the ar- rangement about that axis? (b) If we approximated the arrangement as being a uniform rod of mass M and length L, what percentage error would we make in using the formula in the Moodle table for a rod to calculate the rotational inertia? ooooooooooooooo

= (b) The figure below shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.0000 m and (total) mass M 100.0 mg. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point O. (a) What is the rotational inertia of the ar- rangement about that axis? (b) If we approximated the arrangement as being a uniform rod of mass M and length L, what percentage error would we make in using the formula in the Moodle table for a rod to calculate the rotational inertia? ooooooooooooooo

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)...

See similar textbooks

Related questions

Q: Two wheels of moment of inertia 2.0 kg m and 1.0 kg.m are set in rotation with angular speed 6.4…

Q: (c) Astronomical observations indicate that the rotational velocity follows a different behaviour:…

A: Vobserved - Black Vcalculated – Red, Blue

Q: A 2 kg ball with a radius of 0.35 meters is initially at rest. The rotational inertia equation for…

A: We know that Torque= Ta=Fr

Q: A sanding disk with rotational inertia 4.2 x 103 kg-m² is attached to an electric drill whose motor…

A: Rotational inertia (I) = 0.0042 kg m-2Torque (T) = 38 N.m time (t) = 29 ms = 0.029 s

Q: Consider a cylinder of length L and radius R with density given by p(r) = po"/R: a) What is the mass…

A: (a) Let the given cylinder’s volume be denoted by V. Its total mass (M) can be determined by…

Q: On the topic of rotational motion, the gyroscope flywheel rotates in a circular motion horizontally…

Q: Figure (a) shows a disk that can rotate about an axis at a radial distance h from the center of the…

Q: The rotational inertia of a collapsing spinning star changes to 1/9 its initial value. What is the…

Q: A wheel of radius 0.282 m, which is moving initially at 37.9 m/s, rolls to a stop in 205 m.…

Q: A hula-hoop with a radius of 0.35 m is rotating at 15 radians per second. It weighs 1.7 kg. (A) How…

A: We know,v=rωwhere,v is linear velocityr is radius of hula hoopω is angular…

Q: A disk is constructed so that it can be made to rotate about an axis through it's center of mass…

A: Given: A disc is rotating about an axis through CM, rim(R), halfway b/w R & CM(H).

Q: The person whose leg is shown in figure below kicks his leg by exerting a 2000N force with his upper…

A: We are given the force acting. We are also given the lever arm length. We first find the torque. We…

Q: A car travelling at 108 km/h . Given the the tires on the car have radius of 40 cm , what is their…

A: Given data: The speed of the car is V=108 km/h. The radius of the tire of the car is R=40 cm.…

Q: The 51-kg flywheel has a radius of gyration of ko= 300 mm about its center of mass. (Figure 1) If it…

Q: A potter's wheel is a horizontal disk with a moment of inertia of 0.85 kg m2 that rotates with a…

A: Initial moment of inertia (I1)= 0.85 kg m² Initial angular velocity (w1)= 2 rad/s Mass of the dense…

Q: Consider the 15.0 kg motorcycle wheel shown in the figure. Assume it to be approximately an annular…

Q: Write a question requires a mathematical calculation about the rotational displacement of an object…

Q: Calculate the moment of inertia about the z-axis, IZ, for a mass m = 3 mg, that rotates about the…

A: Given: mass of the object (m) = 3 kg the radius of rotation (r) = 3 inches = 3 x 0.0254 =…

Q: A bicycle tire is spinning counterclockwise at 2.40 rad/s. During a time period At = 1.05 s, the…

Q: A track is mounted on a large wheel that is free to turn with negligible friction about a vertical…

Q: A 200g toy car is placed on a narrow 30cm radiustrack with wheel grooves that keep the car moving in…

Q: Consider a science exhibit consisting of a wooden pole of length 1.3 m and mass 4.0 kg as shown in…

A: Given : mr=4kg m1=2.1kg m2=4.2kg L=1.3m This problem will…

Q: An anemometer for measuring windspeed consists of four small metal cups, each of mass 120 g, mounted…

Q: After all the metal has unwound from the roller, the student measures the radius R and the angular…

A: Part (f) Basic Details According to the law of conservation of linear momentum, the momentum of the…

Q: A bicycle tire is spinning clockwise at 3.70 rad/s. During a time period At = 2.05 s, the tire is…

A: Given that,∆t=2.05 secInitial angular speed CW, ω0=-3.70 radsFinal angular speed CCW, ωf=3.70 rads

Q: Small bodies of mass m, and m₂ are attached to opposite ends of a thin rigid rod of length L and…

Q: A rope with a negligible mass has two blocks that are suspended over a pulley, m, and M, as shown in…

A: Apply Newton’s second law on both the masses and solve for the tensions (on the left side and the…

Q: A bicycle tire is spinning clockwise at 3.10 rad/s. During a time period At = 1.70 s, the tire is…

A: Given that:- Time duration is given as 1.70sec

Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

(b) The figure below shows an arrangement of 15 identical disks that
have been glued together in a rod-like shape of length L = 1.0000
m and (total) mass M 100.0 mg. The disks are uniform, and the
disk arrangement can rotate about a perpendicular axis through its
central disk at point O. (a) What is the rotational inertia of the ar-
rangement about that axis? (b) If we approximated the arrangement
as being a uniform rod of mass M and length L, what percentage
error would we make in using the formula in the Moodle table for a
rod to calculate the rotational inertia?
L
ooooooooooooooo

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Angular speed, acceleration and displacement

Learn more about

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

Similar questions

A mass m rotates at constant speed v at a radius of R from the rotational eaxis. A force F provides centripetal force Fc . If you double mass, radius and v, the force needed to keep the mass in circular motion would (a) stay the same (b) double (c) halve (d) quadruple
What is the angular momentum of a 0.315 kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 12.0 rad/s ? Express your answer using three significant figures and include the appropriate units.
A uniform solid ball rolls without slipping down a plane which is inclined at 31° to the horizontal. If the ball has a radius r=0.4m, a mass m=0.1 kg and starts from rest, find: a) the speed of the ball after it travels 2m down the incline. b) at this point, what is the angular momentum of the ball? c) If the coefficient of friction between the ball and the plane is 0.25, what is the maximum angle of inclination that allows the ball to roll without slipping?
The ball has a mass of 1 kg and is confined to move along the smooth vertical slot due to the rotation of the smooth arm OA. The rod is rotating with a constant angular velocityd slot at any instant. Which one of the following is (are ) incorrect answers ? =2 rad/s. Assume the ball contacts only one side of the ion e-2 rads Select one or more: There is only one contact force on the ball that is acting perpendicular to the rod. There are two contact forces on the ball: one is acting perpendicular to the wall, and the other is perpendicular to the rod. The path of the ball is given by r 0.5 sec 0. The acceleration along the 0 increasing direction is a, tan 6 sec 00 The normal reaction to the ball by the rod is given by the equation N gcos+ a, whiere ap s the acceleration along the 6 increasing direction.
A solid metal disk with moment of inertia I, radius R, and mass m1 can rotate freely about a frictionless axis passing through its center. A light string is wrapped around the disk and connects to a hanging mass m2. The hanging mass is released from rest at a distance d above the ground and accelerates downward with acceleration awhile the disk rotates through an angle q. a) Find an expression for the angular accelerationaof the diskin terms of m2, I, R, and any necessary constants. b) Find an expression for the time it takes for the hanging mass to reach the ground. Write your answer in terms of q, a, and any necessary constants. c) Find an expression for the angular velocity of the disk just before the hanging mass hits the ground. Write your answer in terms of q, a, and any necessary constants.
A space craft may be modeled as a uniform disk. Suppose the disk shaped craft has a mass of 2500 kg and a radius of 5.67 ngedalla par pplica meters. (a) What is the moment of inertia of the spacecraft? (b) Two rocket engines on opposite sides of the craft each apply an identical tangential force to impart a uniform angular acceleration in the counterclockwise sense. Suppose the craft acceleration from rest to an angular velocity of 1.00 revolutions per second in the counter clockwise sense over a period of 30.0 seconds. What is this final angular velocity in radians per second? (c) What is the angular acceleration of the craft over the period of uniform angular ac- celeration? (d) What net torque is needed to achieve the angular acceleration in part (c)? (e) What force is applied by each rocket engine during the period of uniform angular accel- eration?
A light rigid bar of length, l = 1m, is attached to two particles, with masses m1 = 4 kg and m2 = 3 kg, at their ends. The combination rotates in the xy plane about an axis through the center of the bar, right figure. Determine the angular momentum of the system about the origin when the speed of each particle is 5 m / s.
Can someone explain this?
Suppose a 0.230 kg ball is thrown at 18.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in the figure below. V (a) Calculate the final linear velocity (in m/s) of the person, given his mass is 92.0 kg. m/s (b) What is his angular velocity (in rad/s) if each arm is 8.00 kg? You may treat the ball as a point mass and treat the person's arms as uniform rods (each has a length of 0.810 m) and the rest of his body as a uniform cylinder of radius 0.170 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center. rad/s (c) Compare the initial and final total kinetic energies. O Initial kinetic energy is the same as final kinetic energy. O Initial kinetic energy is less than final kinetic energy. O Initial kinetic energy is greater than final kinetic energy.