Calculating Impulse on a Ball: Mass, Radius & Speed

[jeremy222]

Homework Statement

Lets say I have a ball rolling on a flat frictionless surface. I give it an impulse to set it into rolling without slipping at a speed u. The mass of the ball is m and the radius is a. How large is the impulse and where is it applied

Homework Equations

I guess linear and angular momentumn

The Attempt at a Solution

Well i know linear impulse is the change in linear momentum and for angular impulse it is the change in angular momentum. However, I am confused about what impulse is. Is it the addition of linear and angular impulse? Moreover, I think this question will have a range of answers since i doubt it is only one spot where I will apply the impulse and get rolling without slipping but I am just confused.

 

[tiny-tim]

hi jeremy222!

How large is the impulse and where is it applied
…
Well i know linear impulse is the change in linear momentum and for angular impulse it is the change in angular momentum. However, I am confused about what impulse is. Is it the addition of linear and angular impulse?

every impulsive force has a linear impulse, and also an angular impulse (which depends on whatever point you choose to calculate it about)

the question only asks for the linear impulse (and its position)

Moreover, I think this question will have a range of answers since i doubt it is only one spot where I will apply the impulse and get rolling without slipping but I am just confused.

friction is not an implusive force, so there will be slipping unless you get everything exactly right!

 

[rcgldr]

However, I am confused about what impulse is.

Force x time, and it equals the total change in momentum, linear + angular, even if the impulse itself is only linear.

a ball ... on a flat frictionless surface. ... I doubt it is only one spot where I will apply the impulse and get rolling without slipping.

Assuming that the direction of the impulse is horizontal (parallel to the frictionless surface), then there is only one point that will result in the ball "rolling" on a frictionless surface. You also have to assume that the impulse is applied in an instant and with infinite friction on the ball at the point of application of the impulse, in order to result in a change in angular momentum. It might be easier to visualize the sphere similar to a yo-yo, where the sphere is divided into two halves connected by a massless hub with an infinitely thin string wrapped around the hub. The string is pulled horizontally and it unwinds from the top of the hub. For the sphere to end up "rolling" on a frictionless surface as the string is pulled, the hub has to have a specific radius versus the radius of the sphere.