# Rolling without slipping on application of impulse

• nerdvana101
In summary, an impulse points the sphere in a particular direction, causing pure rolling motion. The point of contact is the center of rotation and the linear velocity matches the angular velocity if the sphere is resting on a frictionless surface.
nerdvana101
HI,

I am having some trouble understanding the effects of an impulse on rolling motion, particularly without slipping.

For eg, if we take a sphere of radius R and mass M, then what is the point h above the centre C at which when an impulse is imparted, will cause pure rolling motion? (i.e., without slipping)

I have racked my brain two days over this. I think I am seriously missing something.

hi nerdvana101!

if there's rolling without slipping, the centre of rotation is the point of contact, so you can use angular momentum about that point to find the angular velocity

then do impulse = m∆vc.o.m to find if the linear velocity matches the angular velocity

This problem doesn't make much sense if the sphere is resting on a surface with a high amount of friction, since it will roll with the impulse applied just about anywhere. I assume the idea here is that the surface is frictionless, and the goal is to locate the impulse so that the surface speed due to angular rotation always equals the linear speed as the sphere accelerates. The linear force produces the same linear acceleration no matter where the impulse is located, so only the angular acceleration is dependent on the location of the impulse. The angular acceleration = torque / (angular inertia), and torque = force x radius of the point of appliciation of the impulse. You could think of the sphere as being a yo-yo with a massless hub and a string wrapped around the hub, so that the string tension is how the impulse is imparted at some radius from the center of the sphere's axis of rotation.

This is very important in billiards and pool. If the pool cue hits the center of the billiard ball, the ball will slide because no angular momentum is transferred to the ball, except by sliding on the table. The cue has to hit the ball above the midpoint to impart some angular momentum to the ball. The problem is to find the impulse point of impact such that (as tiny tim pointed out) the angular velocity vrot = Rdθ/dt and the linear velocity vlinear = p/m of the ball are equal.

tiny-tim said:
hi nerdvana101!

if there's rolling without slipping, the centre of rotation is the point of contact, so you can use angular momentum about that point to find the angular velocity

then do impulse = m∆vc.o.m to find if the linear velocity matches the angular velocity

Thx tiny-tim. What I forgot to add was the basics of angular momentum -

L at the point of contact = Icomxω + rcomxmxvcom.

THX a lot!

isn't there any option to select the best answer?

## 1. What is rolling without slipping on application of impulse?

Rolling without slipping on application of impulse is a type of motion in which an object, typically a wheel or a ball, moves forward without sliding while also rotating. This occurs when an impulse, or a sudden change in momentum, is applied to the object.

## 2. How does rolling without slipping on application of impulse differ from other types of motion?

Rolling without slipping on application of impulse is different from other types of motion, such as pure rolling or sliding, because it involves both translational and rotational motion. In pure rolling, the object moves forward without rotating, while in sliding, the object moves forward while also sliding or skidding.

## 3. What is the relationship between impulse and rolling without slipping?

The application of an impulse to an object in motion causes a change in its momentum. In the case of rolling without slipping, the impulse causes both translational and rotational motion, resulting in the object moving forward without slipping or sliding.

## 4. What are some real-world examples of rolling without slipping on application of impulse?

Some examples of rolling without slipping on application of impulse include a car's tires rolling on the road, a bowling ball rolling down a lane, and a person riding a bike or skateboard. In each of these cases, an impulse is applied to the object, causing it to move forward without slipping or sliding.

## 5. How is rolling without slipping on application of impulse important in science and engineering?

Rolling without slipping on application of impulse is important in science and engineering as it is a fundamental concept in understanding the motion of objects. It is also a crucial concept in the design of various machines and mechanisms, such as gears, wheels, and pulleys, which rely on rolling without slipping for efficient and controlled movement.

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