Problem 1. A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M. It is mounted so that it rotates on a fixed, horizontal axle. The friction force between the axle and M the spool causes counterweight of mass m is connected to the end of a string wound around the spool. The counterweight falls initially from rest to a position y at time t. an average torque Tf. A R/2 т (a) Use the integration method to find the moment of inertia of the spool as a function of M and R. R/2 mg- T (b) Show that y=4t? 8 т+5 М

Problem 1. A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M. It is mounted so that it rotates on a fixed, horizontal axle. The friction force between the axle and M the spool causes counterweight of mass m is connected to the end of a string wound around the spool. The counterweight falls initially from rest to a position y at time t. an average torque Tf. A R/2 т (a) Use the integration method to find the moment of inertia of the spool as a function of M and R. R/2 mg- T (b) Show that y=4t? 8 т+5 М

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: motor rotating a workshop grinding wheel at 1.14 x 102 rev/min is switched off. Assume the wheel has…

Q: The 5-kg cylinder is initially at rest when it is placed in contact with the wall B and the rotor at…

Q: A 2.5 kg disk of radius 0.25 m is free to rotate about an axis at its center. What force, exerted as…

A: Given that,Mass of disk : m = 2.5 (kg)Radius : r = 0.25 (m)Angular acceleration : α = 15…

Q: A circular disk with a radius of 0.44 m is subject to 2 tangentially applied forces. The disc is…

A: The magnitude of the torque on the object is given by Where r = distance from the axis, F = Force…

Q: Q20. An open tub rolls across a frictionless surface. As it rolls, rain falls vertically into the…

A: Given:: Quantitative explaination

Q: 1. The tyre is freely rotating at the rate of 50 rad/s and moving forwards (exactly like rotation of…

A: Here given the tyre is rotating at a rate 50 rad/s . The radius of the tyre is 60 cm. There are A,O…

Q: A dentist's drill starts from rest. After 4.10 s of constant angular acceleration it turns at a rate…

A: The initial angular speed is zero. The final angular speed in rad/s can be obtained as ωf=2.80×104…

Q: An electric motor rotating a workshop grinding wheel at 1.04 x 102 rev/min is switched off. Assume…

A: initial angular velocity, wo = 1040 rpm = 108.8 rad/s angular acceleration = 2.02 rad/s2 final…

Q: F3 F1 F2

A: Given, Radius, r=0.53m F1=14.7N F2=11.1N F3=11.5N Net torque is given by, τnet=∑r×F

Q: A bicycle wheel, of radius 0.3300 m and mass 3.000 kg (concentrated on the rim), is rotating at…

A: Given: The radius of the wheel is 0.33 m. The mass of the wheel is 3 kg. The initial angular speed…

Q: A coin with a diameter of 2.00 cm is dropped on edge onto a horizontal surface. The coin starts out…

A: Given diameter of the coin d=2.00cm Therefore its radius r=d/2=1.00cm=0.0100m Initial angular speed…

Q: 8. Suppose that the vector in problem 2. above represents a 30 mph wind. Sera is piloting an…

Q: How much torque would it take to make the wheel speed up from rest to 1.5 rev/sec in 10 sec? b. Now…

A: The moment of inertia of a rigid body is the sum of the products of the masses of all the particles…

Q: A 2.5 kg disk of radius 0.25 m is free to rotate about an axis at its center. What force, exerted…

Q: The 19-cm diameter disk in can rotate on an axle through its center. 30 N 45° 5 cm 5 cm 20 N X 30 N…

Q: L L L/4 L/2 i30€ Direction: Magnitude: Direction: Magnitude: 30

Q: circular disk with a radius of 0.43 m is subject to 2 tangentially applied forces. The disc is fixed…

Q: A solid sphere of radius 6.00 cm and mass 7.00kg is mounted on an axle through its center. a.…

A: It's a concept of Torque.

Q: A circular disk with a radius of 0.37 m is subject to 2 tangentially applied forces. The disc is…

A: Given data: Radius of circular disk (R) = 0.37 m Force (F1) = 4.9 N, applied at outer edge Force…

Q: An electric motor rotating a workshop grinding wheel at 1.12 x 102 rev/min is switched off. Assume…

A: a)The time taken to stop the wheel is 6.17sb)The angular displacement is 36.15radExplanation:Step…

Q: A truck wheel with radius R= 500 cm has an initial angular velocity of 12 rad/s, and is slowing down…

A: The final angular velocity is zero. The wheel is decelerating. Let, R=500 cm=5.0 mωi=12 rad/sωf=0…

Q: Assignment 3 1. 30 N - 30 N 5.0 5.0 ст cm 20 N 20 N The 20-cm-diameter disk can rotate on an axle…

A: Introduction: Torque is a twisting force that is responsible for the rotation of object, and torque…

Q: A child of mass 32.6 kg rides a broken 13.0-kg merry-go-round in the shape of a hoop of radius 4.12…

Q: A dentist's drill starts from rest. After 4.00 s of constant angular acceleration it turns at a rate…

Q: A particle rotates with constant speed in a circle. Let t be the net torque on the particle and F…

Q: A uniform disk of radius 0.551 m and unknown mass is constrained to rotate about a perpendicular…

A: The objective of the question is to determine the mass of the disk given the radius, the tangential…

Q: enti

A: GivenF=5 Nr=36 cm=0.36 mWheel starting from restωo=0θ=10 rev=10×2π radt=4 s

Q: String is wrapped around the outer rim of a solid uniform cylinder that is free to rotate about a…

Q: A meter stick has a pivot placed ate 30 cm. The following masses are placed at the following…

Q: A disc with a radius of 0.53 m is fixed to rotate about its center. Three forces act on the object…

A: Given: The force F1 is 14.7 N. The force F2 is 11.1 N. The force F3 is 11.5 N. The angle is 34.3…

Q: During the launch from a board, a diver's angular speed about her center of mass changes from zero…

A: Given data: ωi=0ωf=6.9 rad/sTimr (t) = 310 msI=12 kg.m2 Need to determine the magnitude of the…

Q: The 22-cm-diameter disk pictured can rotate on an axle through its center. What is the net torque…

Q: An electric motor rotating a workshop grinding wheel at a rate of 1.07 x 102 rev/min is switched…

Q: In a downtown office building, you notice each of the four sections of a rotating door has a mass of…

A: Mass of each door m= 80 KgAngular acceleration α=0.500 rad/s2Applied Force F=66 N

Q: A turntable must spin at 33.3 rev/min (3.49 rad/s) to play an old-fashioned vinyl record. How much…

A: Initial angular speed is Final angular speed is Angular displacement is Diameter of the disk is Mass…

Q: A turntable must spin at 33 turntable is to reach its final angular speed in 2.30 revolutions,…

A: Expression for angular acceleration of the disk is α=ωf2-ωi22∆θ Expression for torque τ=Iα=12md24α…

Q: 20. The 57.2cm diameter disk rotates counterclockwise on an axle through its center. F1=42.6N,…

Q: In a downtown office building, you notice each of the four sections of a rotating door has a mass of…

Question

Problem 1.
A uniform, hollow, cylindrical spool has inside
radius R/2, outside radius R, and mass M. It is
mounted so that it rotates on a fixed, horizontal
axle. The friction force between the axle and
M
the spool causes
counterweight of mass m is connected to the
end of a string wound around the spool. The
counterweight falls initially from rest to a
position y at time t.
an average torque Tf. A
R/2
т
(a) Use the integration method to find the
moment of inertia of the spool as a function of
M and R.
R/2
mg- T
(b) Show that
y=4t?
8 т+5 М

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

Step 5

Step 6

Step 7

Step 8

Step 9

Trending now

This is a popular solution!

Step by step

Solved in 9 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A coin that is tossed straight up into the air. After it is released, it moves upward, reaches its highest point and falls back down again. Use one of the following choices (A through G) to indicate the acceleration of the coin during each of the stages of the coin's motion described below. Take up to be the positive direction. Answer choice J if you think that none is correct. A. The acceleration is in the negative direction and constant. B. The acceleration is in the negative direction and increasing. C. The acceleration is in the negative direction and decreasing. D. The acceleration is zero. E. The acceleration is in the positive direction and constant. F. The acceleration is in the positive direction and increasing. G. The acceleration is in the positive direction and decreasing. The coin is moving downward. A OF ΟΕ B
To a light beam (of negligible mass), two antiparallel forces are applied, as shown in the figure. These forces cause a net torque equal to 7.5 Nm (and with the same direction as that caused by F2) at the left end of the beam. If F1 = 10.7 N and F2 = 5.4 N, determine the distance "l" that separates them
A thin hoop of radius 0.6 m is rotating about its central axis with an angular velocity of +26 rad/s. At t = 0, a force F is applied tangentially to the rim of the hoop, and 4 s later, the hoop comes to a stop. The rotational inertia of the hoop about its central axis is 0.3 kg-m². a. What is the angular acceleration of the hoop while the net torque is applied? Include a plus/minus sign to indicate direction.
The wheel and axle have forces applies tangentially as shown in the figure. There is also a frictional torque of 0.02 Nxm on the wheel, once the wheel starts moving. The radius of the axel is 20 cm and the radius of the wheelis 60 cm and F1 = 2.4 N, F2 = 3.0 N and F3 = 1.2 N. a. Calculate the net torque on the moving wheel due to the applied forces F1 F2 and F3. b. What direction of rotation would the applied forces cause? Explain. c. What is the direction of frictional torque? Explain. d. Calculate the net torque on the wheel and axle.
The radius of a park merry-go-round is 2.5 m. To start it rotating, you wrap a rope around it and pull with a force of 260 N for 20 s. During this time, the merry-go-round makes one complete rotation. (a) Find the angular acceleration of the merry-go-round. rad/s2 (b) What is the magnitude of the torque exerted by the rope on the merry-go-round? N-m (c) What is the moment of inertia of the merry-go-round? kg-m2 eBook
Two tangential forces F1 = 25 N and F2 = 10 N are applied to the rim of a solid cylinder of radius R = 0.2 m. The cylinder starts to rotate from rest, and reaches angular speed of 50 rpm in 5 seconds. Find the mass of the cylinder.
Calculate the net torque on the disk of diameter 0.350 m with respect to an axis passing through the center as shown in the figure. The 11.9 N force is perpendicular to the edge of the disk, while the 8.50 N force is tangent to the disk. 11.9 N 40.0° 14.6 N 8.50 N O 6.26 N.m O 5N.m O 4.5 N.m O 24 N.m 0.350 m
A circular disk with a radius of 0.37 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. F1 = 4.7 N applied at the outer edge of the disc. F2 = 3.2 N applied at a distance of 0.3 from the center of the disc. What is the net torque on the disc?
A circular disk with a radius of 0.42 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. F1 = 4.4 N applied at the outer edge of the disc. F2 = 3 N applied at a distance of 0.2 from the center of the disc. What is the net torque on the disc?
On a playground, there is a merry-go-round. In order to get it moving, Bonnie applies a force of 17 N. The merry-go-round measures 5.3 m from the axis of rotation to the edge where Bonnie applies her force. Assuming she applies her force perpendicularly to a line drawn from the axis of rotation, what is the magnitude of the torque t Bonnie imparts to the merry-go-round? T = N.m
The blades of a medium size wind turbine rotate at a maximum rate of 20.6 rev/min. The total moment of inertia of the blades is 1701 kg.m. What is the torque (in N.m) required to rotate the blades from rest to the maximum rotation rate in 5 minutes?
A string is wrapped around a thin-walled cylinder pulley of radius 11.9 cm and mass of 13 kg. If the string is pulled by a force that is tangent to a point on the rim of the pulley, how much force is exerted to cause it to rotate at a constant rate of 4.82 rad/s²? The moment of inertia for thin-walled cylinder is I = mr². O 7.46 N Q 527N Q 62.7N 0.887 N