A 2.2 kg hoop 1.2 in diameter is rolling to the right without slipping on a...

A 2.2 kg hoop 1.2 in diameter is rolling to the right without slipping on a horizontal floor at a steady 2.6 rad/s. A uniform cylinder with its outer radius two times it’s inner radius with the same mass, same diameter as the hoop and also rolls without slipping with the same angular frequency. What is the ratio of rotational kinetic energies between the hoop and the uniform cylinder? What is the ratio of the rotational frequency between the hoop and uniform cylinder for the two to rotate with the same angular momentum about an axis through their center of mass?

Solutions

Expert Solution

The mass of hoop =, radius of hoop = ,angular frequency of hoop =

Moment of inertia of hoop

Rotational kinetic energy of hoop

The mass of cylindrical shell = ,Outer radius of cylindrical shell , Inner radius of cylindrical shell ,

Moment of inertia of cylinder

Rotational kinetic energy of cylinder is

Ratio of rotational kinetic energies of hoop and cylinder is

--------------------

If the hoop and cylinder has same angular momentum,

Ratio of rotation frequency between the hoop and cylinder is

--------------------------

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A hoop of mass M=400.g and radius R=20.0 cm is rolling without slipping in clockwise direction...

A hoop of mass M=400.g and radius R=20.0 cm is rolling without slipping in clockwise direction down an incline plane with the incline angle ? = 20? . 1. How much work is done by frictional force acting on the hoop on (1) translation, (2) rotation of the hoop? Show all work so that your final answer is justified. 2. How much is ???ℎ?? on the hoop? Explain by using your answer from part 1, and whatever other argument you...

1. A hollow sphere (mass 2.75 kg, radius 19.9 cm) is rolling without slipping along a...

1. A hollow sphere (mass 2.75 kg, radius 19.9 cm) is rolling without slipping along a horizontal surface, so its center of mass is moving at speed vo. It now comes to an incline that makes an angle 25.6o with the horizontal, and it rolls without slipping up the incline until it comes to a complete stop. Find a, the magnitude of the linear acceleration of the ball as it travels up the incline, in m/s2. 2. At t =...

Problem: a unifiorm hoop of mass m and radius r rolls without slipping on a fixed...

Problem: a unifiorm hoop of mass m and radius r rolls without slipping on a fixed cylinder of radius R. if the hoop is stats rolling from rest on top of the bigger cylinder, use the method of Lagrange multipliers to find the point at which the hoop fall off the cylinder. Question: I know how to derive Lagrange equeation. but to use the method of Lagrange multipliers, i have to finde constrain. solution says that f1, f2 are constrain....

A uniform hoop of mass M and radius R rolls down an incline without slipping, starting...

A uniform hoop of mass M and radius R rolls down an incline without slipping, starting from rest. The angle of inclination of the incline is θ. a. After moving a distance L along the incline, what is the angular speed ω of the hoop? b. If the coefficient of static friction between the hoop and the incline is µs = 1/3, what is the greatest possible value of θ such that no slipping occurs between the hoop and the...

Consider a cylinder rolling, without slipping, on an inclined flat surface (a ramp) that forms an...

Consider a cylinder rolling, without slipping, on an inclined flat surface (a ramp) that forms an angle  = 30 º with respect to the horizontal direction. An external force F = 10 N parallel to the ramp is pushing the cylinder in the uphill direction, without creating any torque (that is, the force is acting directly on the center of mass of the cylinder). If the cylinder is released at a time t = 0 with a linear velocity...

A hoop, a solid disk, and a solid sphere, all with the same mass and the same radius, are set rolling without slipping up an incline, all with the same initial kinetic energy.

A hoop, a solid disk, and a solid sphere, all with the same mass and the same radius, are set rolling without slipping up an incline, all with the same initial kinetic energy. Which goes furthest up the incline? The hoop The disk The sphere They all roll to the same height Briefly explain your answer to the previous question. The same three objects as in the previous question are set rolling without slipping up an incline, all with the same initial linear speed. Which goes farthest...

A disc and solid sphere are both rolling without slipping so that both have a kinetic...

A disc and solid sphere are both rolling without slipping so that both have a kinetic energy of 294. What is the translational kinetic energy of the disc ? What is the translational kinetic energy of the solid sphere ?

1. A solid uniform cylinder is rolling without slipping. What fraction of this cylinder's kinetic energy...

1. A solid uniform cylinder is rolling without slipping. What fraction of this cylinder's kinetic energy is rotational? (Note: the moment of inertia of a cylinder of mass M and radius R rotating about its central axis is 0.5MR2.) A 1/3 B 2/3 C 1/2 D 1/4 E 3/4 2. A public art installation consists of three 25-kg glass sculptures hung side-by-side with steel wires of length 1.00 m, 2.00 m and 3.00 m. If the wires all have the...

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 15.0 ∘...

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 15.0 ∘ above the horizontal. After it has rolled 4.50 m along the ramp, what is the magnitude of the linear acceleration of its center of mass?

a 1m radius cylinder with a mass of 852.9 kg rolls without slipping down a hill...

a 1m radius cylinder with a mass of 852.9 kg rolls without slipping down a hill which is 82.1 meters high. at the bottom of the hill what friction of its total kinetic energy is invested in rotational kinetic energy

Subjects