The radius of a roll of paper is 7.6 cm and its moment of inertia is 2.9 x 10^3 kg.m^2. A force...
Question:
The radius of a roll of paper is 7.6 cm and its moment of inertia is 2.9 x 10{eq}^3 {/eq} kg.m{eq}^2 {/eq}. A force of 3.2 N is exerted on the end of the roll for 1.3 s, but the paper does not tear so it begins to unroll. A constant friction torque of 0.11 N.m is exerted on the roll which gradually brings it to a stop. Assume that the paper's thickness is negligible.
a. Calculate the length of paper that unrolls during the time that the force is applied (1.3 s).
b. Calculate the length of paper that unrolls from the time the force ends to the time when the roll has stopped moving.
Torque
The term torque refers to a physical quantity of vectorial character that depends on 3 things: the modulus of the applied force, the direction of the force, and the distance from the point of force application to the axis of rotation.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerVariables:
R is the radius of the cylinder (paper roll)
I is the moment of inertia
F is the applied force
{eq}\tau_F{/eq} is the torque of the...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Rotational Inertia | Definition, Formula & Examples
from
Chapter 7 / Lesson 5
7.6K
In this lesson, understand what is rotational inertia. See rotational inertia examples to learn how to find rotational inertia using the rotational inertia formula.
Related to this Question
- The radius of the roll of paper is r and its moment of inertia is I. A force F is exerted on the end of the roll of time tpull, but the paper does not tear so it begins to unroll. A constant friction
- The radius of the roll of paper shown in the figure is 7.6 cm and its moment of inertia is I = 2.9 x 10^(-3) kg-m^2. A force of 2.9 N is exerted on the end of the roll for 1.1 s, but the paper does no
- The moment of inertia of a solid uniform disk of mass M and radius R is given by the equation I = 1/2MR^2. A disk with a mass of 5 kg and a radius of 2.5 m rolls without slipping down an inclined plan
- A yo-yo (m = 0.0720 kg) with a rolling radius of r = 2.60 cm rolls down a string with a linear acceleration of 6.53 m/s^2, as shown in the figure below. What is the moment of inertia of this yo-yo?
- A uniform cylinder with mass m and radius R is accelerated by a horizontal force T applied through a rope wound around a light drum of radius r < R. The coefficient of static friction is sufficiently large that the cylinder rolls without slipping. Calcula
- A wheel of mass m = 2.76 kg, radius R = 66 cm, and moment of inertia (about its center of mass) Icm = 0.751mR2 is pulled by a string wrapped around its rim. The string exerts a constant horizontal force F = 38 N, and the wheel rolls without slipping. Find
- A disk of radius 0.46 m and moment of inertia 2.1 kg m^2 is mounted on a nearly frictionless axle. A string is wrapped tightly around the disk, and you pull on the string with a constant force of 34 N. a) What is the magnitude of the torque? b) After a sh
- A round object with mass m and radius R rolls down a ramp that makes an angle theta with respect to the horizontal. You can assume there is static friction so that the object rolls without slipping. a) For now, take the moment of inertia of the object to
- Uniform cylinder with mass m and radius R is accelerated by a horizontal force T applied through a rope wound around a light drum of radius r < R. The coefficient of static friction is sufficiently large that the cylinder rolls without slipping. Calculate
- A 3.0-kg sphere with a radius of 6.0 cm rolls from rest without slipping 4.0 m down an incline, reaching a speed of 7.0 m/s after rolling for 5.0 s. What is the torque that the friction interaction be
- A uniform cylinder with mass m and radius R is accelerated by a horizontal force T applied through a rope wound around a light drum of radius r < R. The coefficient of static friction is sufficiently large that the cylinder rolls without slipping. What is
- A 2-m radius, uniform, 50-kg disk has an object of an unknown moment of inertia screwed into its center. A constant external force of 200 N is applied tangentially to the disk's rim. A constant torque due to kinetic friction of 180 Nmrad is present throug
- A grinding wheel of radius 0.370 m rotating on a frictionless axle is brought to rest by applying a constant friction force tangential to its rim. The constant torque produced by this force is 79.2 N.
- A cylinder of mass M and radius R is pulled by a constant force of magnitude F applied at the top horizontally. The cylinder rolls smoothly on the horizontal surface. Assume that M = 10 kg, R = 0.10 m, F = 12 N, and note that the rotational inertia of th
- A uniform cylinder with mass m and radius R is accelerated by a horizontal force T applied through a rope wound around a light drum of radius r < R. The coefficient of static friction is sufficiently large that the cylinder rolls without slipping. What co
- A disk of radius r = 0.50 m is suspended on a fixed frictionless axle through its center. Its moment of inertia about the axle is 0.40 kg*m^{2}. A constant force F = 40 N is applied tangent to the rim
- A constant horizontal force of magnitude 14 N is applied to a wheel of mass 10 kg and radius 0.30 m. The wheel rolls smoothly and the acceleration of its center of mass is 0.6 m/s2. Find the moment of inertia of the wheel through its center of mass?
- A bead of mass M slides without friction on a circular loop of wire in a vertical plane, with the force of gravity pointing toward the bottom of the paper. The wire is rotating at constant angular vel
- In the figure below, a constant horizontal force F_{app} of magnitude 12 N is applied to a wheel of mass 5 kg and radius 0.30 m. The wheel rolls smoothly on the horizontal surface, and the acceleratio
- A constant torque of 25.0 N \cdot m is applied to a grindstone whose moment of inertia is 0.130 kg \cdot m^2. Using energy principles, and neglecting friction, find the angular speed after the grindstone has made 13.5 revolutions.
- A constant horizontal force of 10.0 N is applied to a wheel of mass 10.0 kg and radius 0.35 m. The wheel rolls without slipping on the horizontal surface, and the acceleration of its center of mass is
- A cylinder of mass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle. If it rolls without slipping, find the acceleration of center of mass and the magnitude and the direction of the frictional force. I =
- A yo-yo has rotational inertia of 860 gcm2 and a mass of 150 g. Its axle radius is 3.4 mm, and its string is 90 cm long. The yo-yo rolls from rest down to the end of the string. (a) What is the magnitude of its linear acceleration? (b) How long does it ta
- A Disk having a moment of inertia 100 kg-m2 is free to rotate without friction, starting from rest, about a fixed axis through its center. A tangential force whose magnitude can range from F = 0 to F = 50.0 N can be applied at any distance ranging from R
- A constant torque of 24.0 N \cdot m is applied to a grindstone whose moment of inertia is 0.130 kg \cdot m^2. Using energy principles, and neglecting friction, find the angular speed after the grindstone has made 15.0 revolutions.
- A constant horizontal force of magnitude 9.2 N is applied to a wheel of mass 8.5 kg and radius 0.19 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass ha
- A constant horizontal force fapp of magnitude 10 N is applied to a wheel of mass 10 kg and a radius 0.30m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has a magnitude of 0.60m/s^2. a.) In unit vector nota
- A bead of mass M slides without friction on a circular loop of wire in a vertical plane, with the force of gravity pointing toward the bottom of the paper. The wire is rotating at constant angular ve
- In the figure, a constant horizontal force F_{app} of magnitude 6.5 N is applied to a wheel of mass 6.1 kg and radius 0.52 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has a magnitude 0.42 m/s^2. (a) W
- In the figure, a constant horizontal force F_app of magnitude 9.1 N is applied to a wheel of mass 5.8 kg and radius 0.29 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has a magnitude of 0.99 m/s^2. What
- A 15.8-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.47 \rm{kg \cdot m^2}, and its radius is 0.158 m. When the reel is turning, friction at the axle exerts a torque of magnitude 4.05 Nm on the
- A constant horizontal force of 8.0 N is applied to a wheel of mass 12.0 kg and radius 0.40 m. The wheel rolls without slipping on a horizontal surface, and the acceleration of its center of mass is 0.
- A constant torque of 22.9 Nm is applied to a grindstone whose moment of inertia is 0.168 kgm2. Using energy principles, and neglecting friction, find the angular speed after the grindstone has made 17
- A wheel of radius R is pulled by a rope looped around a frictionless axle. The total mass of the wheel and axle assembly is M and its moment of inertia is I. A constant force of magnitude F moves the
- A 14.0 m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.500 kg.m^2, and its radius is 0.190 m. When turning, friction at the axle exerts a to
- A constant torque of 25.0 N*m is applied to a grindstone whose moment of inertia is 0.130\ kg \cdot m^2. Using energy principles and neglecting friction, find the angular speed after the grindstone has made 15.0 revolutions.
- A yo-yo has rotational inertia of 890 g.cm^2 and a mass of 165 g. Is axle radius is 4.2 mm, and its string is 135 cm long. The yo-yo rolls from rest down to the end of the string. What is the rotational kinetic energy when the yo-yo rolls down 85 cm?
- In the figure, a constant horizontal force \vec{F_{app of magnitude 15 N is applied to a wheel of mass 6.6 kg and radius 0.51 m. The wheel rolls smoothly on the horizontal surface, and the accelera
- A grinding wheel is in the form of a uniform solid disk of radius 6.97 cm and mass 1.96 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.597 N.m that the
- A disk having moment of inertia 96 kg m ^2 is free to rotate without friction, starting from rest, about a fixed axis through its center. A tangential force whose magnitude can range from F=0 to F=5
- A constant horizontal force of 9.0 N is applied to a wheel of mass 12.0 kg and radius 0.35 m as shown in the figure. The wheel rolls without slipping on the horizontal surface, and the acceleration of
- A constant horizontal force of 14.0 N is applied to a wheel of mass 12.0 kg and radius 0.20 m as shown in the figure. The wheel rolls without slipping on the horizontal surface, and the acceleration o
- A 13.9-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.47 kg-m^2, and its radius is 0.159 m. When the reel is turning, friction at the axle exerts a torque of magnitude 3.57 N-m on the reel. If t
- A grinding wheel is a uniform cylinder with a radius of 8.90 cm and a mass of 0.560 kg. (a) Calculate its moment of inertia about its center. (b) Calculate the applied torque needed to accelerate it from rest to 1700 rpm in 5.00 s if it is known to slow
- A disk having moment of inertia 84 kg-m^2 is free to rotate without friction, starting from rest, about a fixed axis through its center. A tangential force whose magnitude can range from F = 0 N to F = 50.0 N can be applied at any distance ranging from R
- A plank of mass 6 kg rides without slipping on two cylindrical rollers each of mass 2 kg and radius 5 cm. The plank is pulled by a constant horizontal force of 6 N. The cylinders roll without slipping
- In the figure, a constant horizontal force \vec{F}_{app} of magnitude 10 N is applied to a wheel of mass 13 kg and radius 0.39 m. The wheel rolls smoothly on the horizontal surface and the acceleratio
- A cylinder of radius R = 0.270 m pivots around its axis with negligible friction. A mass M = 1.51 kg is suspended from a string wrapped around the cylinder and then released. M accelerates downwards at 6.21\ m/s^2. Calculate the moment of inertia of the c
- A grinding wheel is a uniform cylinder with a radius of 9.00 cm and a mass of 0.580 kg. (a) Calculate its moment of inertia about its center. (b) Calculate the applied torque needed to accelerate it from rest to 1,300 rpm in 5.00 s, if it is known to slo
- A constant horizontal force F of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.60 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has a magnitude of 0.60 m/s2. a. In unit-vector notation,
- A wheel with a radius of 4 m rotates on a fixed frictionless horizontal axis where the moment of inertia is 20 kg.m^2. A constant tension of 50 N is maintained on a rope wrapped around the wheel. If the wheel starts at t=0 s at rest, find the unwrapped r
- A 17.0-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.410 kgm2, and its radius is 0.200 m. When turning, friction at the axle exerts a torque of magnitude 3.40 Nm on the reel. If the hose is pul
- A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 35 degree incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by I = \frac{
- A spherical object (with non-uniform density) of mass 30 kg and radius 0.22 m rolls along a horizontal surface at a constant linear speed without slipping. The moment of inertia of the object about diameter is 0.56 M R^2. The object's rotational kinetic e
- A solid cylinder used for smoothing concrete is rolling without slipping along a horizontal surface with a speed of 5.1 m/s. The cylinder has a mass m = 10.3 kg, radius R = 0.68 m, and moment of inertia I = (1/2)mR^2. You bring the cylinder to rest by exe
- A 10-cm diameter, solid, uniform circular disk with mass 0.2 kg rolls, without slipping, starting from rest, down a long 30 degrees incline. It reaches an angular speed of 8 rad/s in 4 s. The distance moved by the center of mass of the disk in 4.0 s is: (
- A 2.5 kg disk with moment on inertia 0.45 kg.m^2 rolls at a velocity of 12 m/s, with rotational kinetic energy 90 J. (a) Find its initial angular velocity. (b) The disk rolls (without slipping) up an
- A solid cylinder used for smoothing concrete is rolling without slipping along a horizontal surface with a speed of 5.4 m/s. The cylinder has a mass m = 69 kg, radius R = 0.58 m, and moment of inertia I = (1/2)mR2. You bring the cylinder to rest by exerti
- A thin, circular hoop with a radius of 0.22 m is hanging from its rim on a nail. When pulled to the side and released, the hoop swings back and forth as a physical pendulum. The moment of inertia of a
- A yo yo with a mass of 0.0900 kg and a rolling radius of r = 2.70 cm rolls down a string with a linear acceleration of 5.60 m/s2. What is the moment of inertia I of this yo yo?
- In the figure given below, a constant horizontal force F_app vector of magnitude 9.1 N is applied to a wheel of mass 5.8 kg and radius 0.29 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has a magnitude o
- A potter's wheel having a radius 0.53 m and a moment of inertia 14 kg m^2 is rotating freely at 47 rev/min. The potter can stop the wheel in 6.5 s by pressing a wet rag against the rim and exerting a radially inward force of 71 N. Find the effective coeff
- A 1 kg wheel, of radius, 2 cm, rolls down along the inclined plane without sliping. The incline makes an angle of 30 degrees with the horizontal, and its length is 2 m. Find the moment of inertia of this wheel, at the end of inclined plane, with 2m/s.
- A uniform circular wheel (I = MR^2) with radius, R = 1.0 m and mass, M = 50.0 kg is spinning at 120 rev/min. At a particular moment of time (that we denote t = 0) the wheel is subjected to a frictional force F = 20.0 N applied tangentially at its rim. (a)
- A tangential force acts on the rim of a 2.0 kilogram disk-shaped wheel (0.50 m radius) and gives the wheel an angular acceleration of 4.8 rad/s^2. Neglect friction and find the magnitude of the force
- A 15 m length of hose is wound around a reel which is initially at rest. The moment of inertia of the reel of 0.44 kg m^2 and its radius is 0.160 m. When the reel is turning, friction at the axle exer
- A yo-yo has a rotational inertia of 1130 g.cm^2 and a mass of 101 g. Its axle radius is 2.02 mm, and its string is 129 cm long. The yo-yo rolls from rest down to the end of the string. (a) What is the
- A grinding wheel is in the form of a uniform solid disk of radius 6.92cm and mass 1.92kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.591Nm that the moto
- In our lab, we roll a non-uniform but cylindrically symmetric cylinder down a rough 20 degrees incline. The cylinder rolls without slipping and has a mass of 8 kg, radius 1.7 m, and moment of inertia
- The moment of inertia about its axis is given as 0.5 mr^2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is ____. a. 2:1 b. 1:1 c. 1:2 d. 1:3
- A grinding wheel in the form of a uniform solid disk of radius 6.4 cm and mass 1.4 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.725 N . m. (a) How long does it take the wheel to reach its operating speed o
- A grinding wheel has the form of a uniform solid disk of radius 7.05 cm and mass 1.97 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.595 N\cdot m that the motor exerts on the wheel. (a) How long does the wh
- A uniform disk of radius .120 m and mass 5.00 kg is pivoted so that it rotates without friction about its axis. A massless string wrapped around the disk is pulled with a force of 20 N. (a) What is the torque exerted on the disk by the 20 N force? (b) W
- A uniform circular disc of radius R rolls without slipping with a constant velocity on a stationary horizontal surface. Find the distance covered by a point P on its circumference in one full rotation.
- A uniform sphere (r = 30 cm) is rolling without slipping on a flat surface at a constant velocity (i.e., v_{cm} is constant). a. Draw the force diagram for the sphere. b. Which force(s) are responsible for the rolling motion? c. Write the equations of
- A wheel with a radius of 4 m rotates on a fixed frictionless horizontal axis where the moment of inertia is 20 kg.m^2. A constant tension of 50 N is maintained on a rope wrapped around the wheel. If the wheel starts at t = 0 s at rest, find the unwrapped
- A pulley, with a rotational inertia of 1.8 \times 10^{-3}kgm^{2} about its axle and a radius of 16 cm, is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F = 0.50t + 0.30t^{2}, where F is in newtons and t in sec
- A uniform disk with mass 38.8kg and radius 0.200m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 25.0N is a
- A thin metal ring with a diameter of 0.6 m and a mass of 1 kg starts from rest and rolls down an inclined plane. Its linear velocity is 5 m/s. Calculate the moment of inertia and kinetic energy of rot
- A uniform disk with mass 41.2 kg and radius 0.300 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 26.0 N i
- Disk 1 (of inertia m) slides with speed 5.0 m/s across a low-friction surface and collides with disk 2 (of inertia 2m) originally at rest. Disk 1 is observed to turn from its original line of motion b
- A uniform disk with mass 37.8 kg and radius 0.260 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force of 31.0
- A uniform disk with mass 6 kg and radius 1.8 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 31.5N is appl
- A uniform solid sphere of radius R, mass M, and moment of inertia I= \frac{2}{3}MR^2 is rolling without slipping along a horizontal surface. Its total kinetic energy is the sum of the energies associated with the translation of the center of mass and rot
- Calculate the moment of inertia of the object shown about an axis coming perpendicularly out of the paper, and passing through the leftmost mass. Give: M = 2 kg, L = 2 m, and the connecting rods are mass-less. Treat the masses as points masses.
- A grinding wheel is in the form of a uniform solid disk of radius 6.97 cm and mass 2.09 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.595 N.m that the motor exerts on the wheel. (a) How long does the wheel
- A grinding wheel is in the form of a uniform solid disk of radius 7 cm and mass 2 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.6 N m that the motor exerts on the wheel. a. How long does the wheel take to
- A 4.0, kg wheel of 20, cm radius of gyration is rotating at 360, rpm . The retarding frictional torque is .12, N.m . Compute the time it will take the wheel to coast to rest.
- A 5 kg uniform disk with a 40 cm radius swings without friction about a nail through a point 10 cm from the rim. It is released from rest from a position with its center above the nail. (a) What is its angular velocity when the center is directly below t
- A wheel of the moment of inertia 0.500 kg-m^2 and radius 20.0 cm is rotating about its axis at an angular speed of 20.0 rad/s. It picks up a stationary particle of mass 200 g at its edge. Find the new angular speed of the wheel.
- A grinding wheel is in the form of a uniform solid disk of radius 6.94 cm and mass 1.91 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.608 Nm that the motor exerts on the wheel. (a) How long does the wheel
- A grinding wheel is in the form of a uniform solid disk of radius 7.00 cm and mass 2.00 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.600 Nm that the motor exerts on the wheel. (a) How long does the wheel
- A string is wrapped around a uniform disk of mass M=1.3kg and radius R=0.08m.(Recall the moment of inertia of a uniform disc is L / 2 / M R 2 .)Four low mass rods are attached to the disc of radius b=
- A uniform solid disk with radius 8 cm has mass 0.7 kg (moment of inertia I = (1 / 2) MR^2). A constant force 12 N is applied as shown. At the instant shown, the amount of string that has wound off the disk is d = 36 cm, and the angular velocity of the dis
- A uniform disk with mass 4 kg and radius 9.7 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 31.5 N is applied to the rim of the disk. The force direction makes
- A tangential force acts on the rim of a 2.0 kilogram disk-shaped wheel (0.50 m radius) and gives the wheel an angular acceleration of 4.8 \frac{rad}{s^2}. Neglect friction and find the magnitude of th
- A circular disc of radius R/2 is cut from a uniform circular disc of radius R (horizontal diameters are same for both the discs). If the mass of the remaining part is M, the moment of inertia of the r
Explore our homework questions and answers library
Browse
by subject