Question

In: Physics

Rotational Inertia –Rolling Kinetic Energy. A solid sphere, a hollow sphere, a hollow cylinder, and a...

Rotational Inertia –Rolling Kinetic Energy.
A solid sphere, a hollow sphere, a hollow cylinder, and a solid cylinder, all of with same mass (M=0.25 kg ) and radius(R= 0.20 m) – are placed at the top of an incline at height (h= 1.5 m ). All the objects are released from rest at the same moment to roll down without slipping.
Hint: search for the rotational inertia formula for each of the rolling object first. Then calculate each of them and list your formulas, solutions, and answer.
a.   Calculate the magnitude of the rotation inertia (moment of inertia) for each object.
b.   Use your answers from part (a) to predict which one reaches to the bottom first List them in the order of arriving to the bottom of the incline.
c.   Find the potential of the objects at the top of the incline.
d.   Use rolling energy to find the speed of each object at the bottom of the incline to verify your answers to part b.
Torque
a. Force of 2.0 N has been applied at angle of 30 ͦ at distance of 80 cm from the pivot point. Calculate the torque.
b. What is the direction of the rotation? Use right hand rule to explain how you determine the direction of the rotation.

Solutions

Expert Solution


Related Solutions

A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder...
A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder of radius R all have the same mass, and all three are rotating with the same angular velocity. The sphere is rotating around an axis through its center, and each cylinder is rotating around its symmetry axis. Which one has the greatest rotational kinetic energy? both cylinders have the same rotational kinetic energy the solid cylinder the solid sphere they all have the same...
A hollow sphere of radius 0.230 m, with rotational inertia I = 0.0739 kg·m2 about a...
A hollow sphere of radius 0.230 m, with rotational inertia I = 0.0739 kg·m2 about a line through its center of mass, rolls without slipping up a surface inclined at 22.5° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 18.0 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 0.840...
A hollow sphere of radius 0.230 m, with rotational inertia I = 0.0323 kg·m2 about a...
A hollow sphere of radius 0.230 m, with rotational inertia I = 0.0323 kg·m2 about a line through its center of mass, rolls without slipping up a surface inclined at 10.2° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 13.0 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 1.40...
A hollow sphere of radius 0.190 m, with rotational inertia I = 0.0218 kg·m2 about a...
A hollow sphere of radius 0.190 m, with rotational inertia I = 0.0218 kg·m2 about a line through its center of mass, rolls without slipping up a surface inclined at 10.8° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 7.90 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 0.600...
A solid sphere, a follow sphere, and a ring (a hollow cylinder) of uniform density, each...
A solid sphere, a follow sphere, and a ring (a hollow cylinder) of uniform density, each with radius 0.24m and mass 2.6kg roll without slipping on a flat surface at an angular speed of 6.1 rad/s. They then roll without slipping up an incline. 1. What is the linear speed of the center of mass of the ring when it is rolling on the flat surface? 2. What happens as the objects roll up the incline? 3. How high up...
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...
2. Which has more rotational inertia: A solid, uniform sphere of mass 100kg, or a mostly...
2. Which has more rotational inertia: A solid, uniform sphere of mass 100kg, or a mostly hollow spherical shell of mass 100kg? a.They both have the same rotational inertia b.Solid Sphere c.Hollow Sphere 3.If a bicycle starts from rest and is pedaled normally until the bike is moving at 6 meters per second across level ground, what kinds of energy have its tires been given? (Select all that apply) a.Rotational Kinetic Energy b.Translational Kinetic Energy c.Gravitational Potential Energy d.Elastic Potential...
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 ?
A solid cylinder, a thin hollow cylinder (with circular cross-section), and a thick hollow cylinder (with...
A solid cylinder, a thin hollow cylinder (with circular cross-section), and a thick hollow cylinder (with a donut cross section), of equal masses radii, are simultaneously released from rest at the top of an inclined plane and roll without slipping down the plane. Which object reaches the bottom of the inclined plane first? A) The solid cylinder B) The thin hollow cylinder C) The thick hollow cylinder D) All objects reach the bottom at the same time Please provide explanation.
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT