# How Do You Calculate the Frictional Torque and Stopping Time of a Rotating Disc?

• phalanx123
In summary, the conversation discusses finding the frictional torque and time taken for a uniform disc with mass m, radius a, and rotating at an angular speed ω to come to rest on a flat horizontal surface with a coefficient of friction μ. The correct method for calculating the frictional torque and time taken is also mentioned.
phalanx123
I.ve been working on this question for two days now but still couldn't get the right answer. could someone help me please?

A uniform disc of mass m and rasius a, rotating at an angular speed ω, is placed on a flat horizontal surface. If the coefficient of friction is μ, find the frictional torque on the disc, and hence calculate the time it takes to com to rest.

Here is my work.

the frictional force on the disc is F=μN=μmg

therefore the frictional torque is T=Fr=μmga

since T also equals to Iα, where I is the moment of inertia and α is the angular acceleration.

Then α=T/I=(μmga)/I

using ω(i)=ω+αt where ω(i) is the final angular velocity and ω is the initial anglar velocity.

Then 0=ω+αt for it to stop

which gives t=ω/α=(ωI)/(μmga) since I for this disc is 1/2ma2

which then gives t=(ωa)/(2μg)

Hi and welcome to PF phalanx123!

phalanx123 said:
A uniform disc of mass m and rasius a, rotating at an angular speed ω, is placed on a flat horizontal surface. If the coefficient of friction is μ, find the frictional torque on the disc, and hence calculate the time it takes to com to rest.

Is your disc placed horizontally on the surface, or is it held vertically?

I'm guessing that the question means the disc is placed horizontally on the surface, while you've worked it out when the disc is kept vertically on the surface, and held in place.

Last edited:
Oh thanks siddharth, No wonder I got the wrong answer. I'll try to do it as placed horizontaly on the surface. Thanks again ^_^

## 1. What is torque on a rolling cylinder?

Torque on a rolling cylinder refers to the rotational force exerted on the cylinder as it rolls on a surface. It is measured in units of Newton-meters (Nm) and is a vector quantity with both magnitude and direction.

## 2. How is torque on a rolling cylinder calculated?

The torque on a rolling cylinder can be calculated by multiplying the force applied to the cylinder by the radius of the cylinder and the sine of the angle between the force and the radius. The formula for torque is T = F * r * sin(theta), where T is torque, F is force, r is radius, and theta is the angle between the force and the radius.

## 3. What factors affect the torque on a rolling cylinder?

The torque on a rolling cylinder is affected by several factors, including the force applied to the cylinder, the radius of the cylinder, the angle between the force and the radius, and the mass and shape of the cylinder. Additionally, the surface on which the cylinder is rolling and any friction between the cylinder and the surface can also impact the torque.

## 4. How does torque on a rolling cylinder affect its motion?

The torque on a rolling cylinder causes it to rotate and change its direction of motion. The direction of the torque determines the direction of rotation, and the magnitude of the torque determines the speed of rotation. In the absence of any external forces, a rolling cylinder will continue to roll with constant speed and direction.

## 5. How is torque on a rolling cylinder different from torque on a stationary cylinder?

Torque on a rolling cylinder is different from torque on a stationary cylinder because the point of contact between the cylinder and the surface is constantly changing as the cylinder rolls. This results in a different distribution of forces and a different direction of motion for the cylinder compared to a stationary cylinder where the point of contact remains fixed.

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