Peoples Physics Concepts

http://www.ck12.org Chapter 9. Rotational Motion

9.6 Rolling Objects

• Solve problems of rolling objects and of objects that are rolling and sliding.

Students will learn how to solve problems of rolling objects and also of objects that are rolling and sliding.

Key Equations

τnet=Στi=Iα=FFrictionRRollingRadius=μFnormalRRollingRadius

Static and Kinetic Friction’

{

fs≤μs|FN| Opposes potential motion of surfaces in contact

fk=μk|FN| Opposes motion of surfaces in contact

Guidance

When an object is rolling without slipping this means thatv=rωanda=rα. This is also true in the situation of a

rope on a pulley that is rotating the pulley without slipping. Using this correspondence between linear and angular

speed and acceleration is very useful for solving problems, but is only true if there is no slipping. Also, know that

when the object is sliding, kinetic friction is in play. When it is rolling, then static friction. Often, an object will start

out rolling and sliding (kinetic friction) until it slows enough that it is rolling without sliding (static friction). One

can set up a condition by forcingv=rωanda=rαin order to find the point where it stops sliding. Finally, when

this rolling object rolls down the incline, it gains kinetic energy and loses potential energy, just like any object going

down an incline. However, for rolling objects the kinetic energy is split between two forms: rotational and kinetic:

KERollingOb ject=^12 mv^2 +^12 Iω^2

Remember, if the object isn’t sliding but perfectly rolling:v=ωr

Example 1

You throw a bowling ball of massmand radiusrwith an initial speedvodown a flat bowling lane with a coefficient
of kinetic frictionμk. Initially, the ball slides down the lane not rotating at all, but after a time∆t, it begins to roll
perfectly without sliding. Find∆tin terms of the values given above.

Solution

We’ll start by drawing an FBD for the bowling ball.