# Which rolls faster a sphere or cylinder?

## Which rolls faster a sphere or cylinder?

Solid cylinders of different mass and radius roll down the incline at the same rate & reach the bottom at the same time. Solid sphere is faster than solid cylinder since sphere has lower moment of inertia, higher translational kinetic energy.

## Does a sphere or cylinder have more rotational inertia?

For cylinder and sphere, if they have the same mass and radius, cylinder has a larger moment of inertia because it is more massive at places away from the center. The sphere will have a greater speed and it will reach the bottom first, because its moment of inertia is smaller.

What relationship exists between torque moment of inertia and the angular acceleration?

Newton’s 2nd law relates force to acceleration. In the angular version of Newton’s 2nd law, torque τ takes the place of force and rotational inertia takes the place of mass. When the rotational inertia of an object is constant, the angular acceleration is proportional to torque.

How is angular acceleration related to torque?

In rotational motion, torque is required to produce an angular acceleration of an object. The amount of torque required to produce an angular acceleration depends on the distribution of the mass of the object. The torque on a given axis is the product of the moment of inertia and the angular acceleration.

### Do all spheres roll at the same speed?

You should find that a solid object will always roll down the ramp faster than a hollow object of the same shape (sphere or cylinder)—regardless of their exact mass or diameter. This might come as a surprising or counterintuitive result! The answer is that the solid one will reach the bottom first.

### Why does a cylinder have more inertia than a sphere?

For a given mass, a hollow cylinder has more material away from the axis than a solid cylinder, so its moment of inertia is higher.

Why does a sphere have less inertia than a cylinder?

Mathematically for a solid sphere it is 2/3MR^2 whereas for a hollow cylinder it is MR^2. Answer: Since, the outer volume of the solid sphere is less than that of the hollow sphere, its moment of inertia is also less.

What is the relationship between torque and angular velocity?

The instantaneous power of an angularly accelerating body is the torque times the angular velocity: P=τω P = τ ω . There is a close relationship between the result for rotational energy and the energy held by linear (or translational) motion.

#### What do you understand by torque and moment of inertia obtain the relation between torque and moment of inertia for a rigid body?

The Torque in rotational motion is equivalent to force in linear motion. It is the prime parameter that keeps an object under rotatory motion. The torque applied to an object begins to rotate it with an acceleration inversely proportional to its moment of inertia.

#### Are torque and acceleration the same?

Torque is the measure of how much force causes an object to rotate. Typically measured in pounds per foot, an engine’s torque value determines its acceleration. They happen when the car has enough torque to support that kind of rapid acceleration.

What is relation between Ke sphere and Ke disc?

A disc and a sphere of the same mass and radius are rolling. Their kinetic energies are equal.

Do spheres roll faster than disks?

You should find that a solid object will always roll down the ramp faster than a hollow object of the same shape (sphere or cylinder)—regardless of their exact mass or diameter. The answer is that the solid one will reach the bottom first.

## Can a sphere and a cylinder have the same torque?

11. Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre.

## How do torques of the same magnitude affect a hollow cylinder?

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?

What is the difference between torque of equal magnitude?

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. having the same mass and radius.

What is torque and Newton’s second law for rotation?

Torque and Newton’s Second Law for Rotation. Torque, also known as the moment of force, is the rotational analog of force. This word originates from the Latin word torquere meaning “to twist”.