variables. Plug and chug into the rotational kinematics equations:
What does this answer mean? Well, if there are 2π (that is, 6.2) radians in one revolution, then 105
radians is about 17 revolutions through which the wheel has turned.
Now, because the wheel has a radius of 0.50 m, the wheel’s circumference is 2πr = 3.1 m; every
revolution of the wheel moves the bike 3.1 meters forward. And the wheel made 17 revolutions, giving a
total distance of about 53 meters.
Is this reasonable? Sure—the biker traveled across about half a football field in 10 seconds.
There are a few other equations you should know. If you want to figure out the linear position, speed,
or acceleration of a spot on a spinning object, or an object that’s rolling without slipping, use these three
equations:
where r represents the distance from the spot you’re interested in to the center of the object.
So in the case of the bike wheel above, the top speed of the bike was v = (0.5 m) (21 rad/s) = 11 m/s,
or about 24 miles per hour—reasonable for an average biker. Note: To use these equations, angular
variable units must involve radians, not degrees or revolutions!!!
The rotational kinematics equations, just like the linear kinematics equations, are only valid when
acceleration is constant. If acceleration is changing, then the same calculus equations that were used for
linear kinematics apply here:
Rotational Inertia
Newton’s second law states that F (^) net = ma ; this tells us that the greater the mass of an object, the harder
it is to accelerate. This tendency for massive objects to resist changes in their velocity is referred to as
inertia.