Homework Answers
Because F is an external force, it will increase the mechanical energy of the system. By energy conservation the mechanical energy is simply the work done by the force F.
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6. Consider the system shown: m, J, R The wheel with mass m, radius R, and rotational moment of i...
Chapter 11, Problem 081 A uniform wheel of mass 10.0 kg and radius 0.400 m is...
Chapter 11, Problem 081 A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center (see the figure). The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg-m2. The wheel is initially at rest at the top of a surface that is inclined at angle 58.4° with the horizontal; the axle rests on the surface while the wheel...
A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center
A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center (see figure . The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg·m2. The wheel is initially at rest at the top of a surface that is inclined at angleθ = 43.6o with the horizontal; the axle rests on the surface while the wheel extends into a...
6. A disk with a mass M, a radius R, and a rotational inertia of I-...
6. A disk with a mass M, a radius R, and a rotational inertia of I- MR is attached to a horizontal spring which has a spring constant of as shown in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk (a) Calculate the maximum translational velocity of the disk in terms of...
[Use g = 10 m/s^2] A non-uniform wheel of mass 5 kg and moment of inertia...
[Use g = 10 m/s^2] A non-uniform wheel of mass 5 kg and moment of inertia 1/3 mR^2 is set on an incline whose height is h = 4 meters and length is L = 20 meters. The wheel is released from rest at the top of the incline and rolls without slipping to the bottom. What is the wheel's translational kinetic energy at the bottom of the incline? What is the wheel's rotational kinetic energy at the bottom of...
* A ball of mass M and radius R has a rotational inertia of · The...
* A ball of mass M and radius R has a rotational inertia of · The ball is released from rest and rolls without slipping down the ramp with no frictional loss of energy. The ball is projected vertically upward off a ramp as shown in the diagram, reaching a maximum height yaz above the point where it leaves the ramp. In terms of h, ymar is
A hollow sphere of radius 0.240 m, with rotational inertia I = 0.0470 kg·m2 about a...
A hollow sphere of radius 0.240 m, with rotational inertia I = 0.0470 kg·m2 about a line through its center of mass, rolls without slipping up a surface inclined at 13.3° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 12.0 J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has moved 0.690...
suppose a wheel with a moment of inertia I=2.5kg*m², a radius of R=40cm, and a mass...
suppose a wheel with a moment of inertia I=2.5kg*m², a radius of R=40cm, and a mass of 6kg were spinning at 4 rad/s before being released. If it rolls without slipping, how fast will it roll? A. 1.92 m/s B. 1.36 m/s C. 1.85 m/s D. 2.17 m/s
We are given a thin wheel of radius r as shown in the figure. The mass...
We are given a thin wheel of radius r as shown in the figure. The mass of the wheel is M and the mass of the spokes is negligible. The wheel rotates about its axis without translational motion at 2 cycles/s. What is the radian frequency of the wheel? If this wheel is now rolling along a road at 3 m/s, then, noting that there is both rotational and translational motion in the wheel, what is its total kinetic energy?
Question 11 A hollow sphere of radius 0.220 m, with rotational inertia I = 0.0728 kg-m2...
Question 11 A hollow sphere of radius 0.220 m, with rotational inertia I = 0.0728 kg-m2 about a line through its center of mass, rolls without slipping up a surface inclined at 33.7° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 36.0 J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has...
1 Consider a cylinder of mass M and radius a rolling down a half-cylinder of radius R as shown in...
question (c), (d), (e), (f) please. Thanks.
1 Consider a cylinder of mass M and radius a rolling down a half-cylinder of radius R as shown in the diagram (a) Construct two equations for the constraints: i rolling without slipping (using the two angles and θ), and ii) staying in contact (using a, R and the distance between the axes of the cylinders r). (b) Construct the Lagrangian of the system in terms of θ1, θ2 and r and two...
Chapter 11, Problem 081 A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center (see the figure). The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg-m2. The wheel is initially at rest at the top of a surface that is inclined at angle 58.4° with the horizontal; the axle rests on the surface while the wheel...
6. A disk with a mass M, a radius R, and a rotational inertia of I- MR is attached to a horizontal spring which has a spring constant of as shown in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk (a) Calculate the maximum translational velocity of the disk in terms of...
[Use g = 10 m/s^2] A non-uniform wheel of mass 5 kg and moment of inertia 1/3 mR^2 is set on an incline whose height is h = 4 meters and length is L = 20 meters. The wheel is released from rest at the top of the incline and rolls without slipping to the bottom. What is the wheel's translational kinetic energy at the bottom of the incline? What is the wheel's rotational kinetic energy at the bottom of...
* A ball of mass M and radius R has a rotational inertia of · The ball is released from rest and rolls without slipping down the ramp with no frictional loss of energy. The ball is projected vertically upward off a ramp as shown in the diagram, reaching a maximum height yaz above the point where it leaves the ramp. In terms of h, ymar is
Question 11 A hollow sphere of radius 0.220 m, with rotational inertia I = 0.0728 kg-m2 about a line through its center of mass, rolls without slipping up a surface inclined at 33.7° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 36.0 J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has...
question (c), (d), (e), (f) please. Thanks.
1 Consider a cylinder of mass M and radius a rolling down a half-cylinder of radius R as shown in the diagram (a) Construct two equations for the constraints: i rolling without slipping (using the two angles and θ), and ii) staying in contact (using a, R and the distance between the axes of the cylinders r). (b) Construct the Lagrangian of the system in terms of θ1, θ2 and r and two...
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