Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

-The wheel of a car has a radius of 20 cm. It initially rotates at 120 rpm. In the next minute it makes 90 revolutions. What is the angular acceleration?_

So the answer is solved by using one of the angular kinematic equations. More specifically delta theta. The problem I am having trouble understanding is the answer which probably stems from my poor fundamentals.

The answer is: (90x2pi) = 4pi(60) + 1/2 (alpha) (60)^2

So where does 90x2pi come from?

share|cite|improve this question
I'm assuming by "in the next minute" you really mean something like, "after a steady acceleration for one minute it reaches 90 rpm" as otherwise your answer isn't right (and the problem becomes a lot more sophisticated). – Carl Brannen Jul 21 '11 at 8:01

The equations you're using are equations for $\theta$, the angle through which the wheel rotates. In physics, we measure angles in radians. There are $2\pi$ radians in a circle, so $90$ revolutions is $90*2pi$ radians.

share|cite|improve this answer

Mixing units is always a recipe for trouble.

As you know, angular acceleration follows similar laws as linear acceleration. Specifically, the angle $\theta$ at time $t$ is given by

$$\theta(t) = \theta(0) + \omega(0) t + \frac12\alpha t^2\tag1$$

which is the analog of

$$x(t) = x(0) + v_0 t + \frac12 a t^2$$

In your case, the angular velocity is expressed in rpm - revolutions per minute - and we usually want to convert to radians per second. $2\pi$ radians in one revolution, 60 seconds in a minute. So

$$\begin{align}\theta(0) &= 0\\ \omega(0) &= 120 * 2 \pi / 60\\ &= 4\pi\\ \theta(t) &= 90\ rev\\ &= 90 * 2 \pi\\ &= 180\pi\\ t &= 60 s\end{align}$$

Solving $(1)$ for $\alpha$:

$$\begin{align} \alpha &= 2\frac{\theta(t) - \omega(0) t}{t^2}\\ &=2\frac{180\pi - 240\pi}{3600}\\ &=-\frac{\pi}{30} \frac{rad}{s^2}\end{align}$$

You could keep the entire thing in revolutions and minutes - then the equation (and the numbers) would be simpler:

$$\alpha = 2\frac{90-120}{1} = -60 \frac{rpm} {min^2}$$

but now you have to get your head around the units of $\frac{rpm}{min^2}$. Once you do, you realize that the speed of the wheel halved - at the end of the minute it's spinning at just 60 rpm (120 - 60 = 60). The fact that the wheel turned 90 revolutions in that minute makes sense now - with linear acceleration, the average speed (90 rpm) is the mid point between the start (120 rpm) and end (60 rpm) speeds...

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.