Radians/second question

Question

I'm stuck on this circle question that my cousin in high school asked me and basically, I need clarification on what I remember should be fine->

1. tire has radius of 42.5 cm rotating 3500 rotations/minute a) rotations/minute into radians/second b) calculate tire traveled in 10 minutes

I'm assuming you divide 60 from 3500 then do something with $2\pi$. then for b) you use distance divided by time?

Answer 1

Hint we have formula to calculate distance its $c\times n=d$ where $c,n,d$ are circumference,number of rotations,distance travelled respectively . For conversion convert rotations to degrees and tgen mutiply by $π/180$ i hope you know conversion from minutes to seconds.

Answer 2

Use unit conversions to find the answers.

a) Do the following conversions to find radians per second: $3500\frac{\text{rev}}{\text{min}} \cdot \frac{1 \text{min}}{60 \text{s}} \cdot \frac{2\pi \text{rad}}{1 \text{rev}},$ which is about $\boxed{366.5}$ radians per second.

b) Find the tire's linear speed using the equation $v = r\omega .$ The value of $\omega$ is the answer found in the first part. The radius is given. Now use $d = vt$ to find the distance traveled. Our answer is $d = r\omega t = 0.425 \cdot 366.5 \cdot 600,$ which is about $\boxed{93462}$ meters.

Answer 3

Any conversion from rpm to rad/s is done as follows: Convert rpm to rps by dividing rpm by 60 $\to {rpm\over 60}={3500\over 60} = {175 \over 3}$

Now you know that the tire makes 58.333 rounds per second. There are $2 \pi$ radians in a complete circle, therfore the tire is rotating at $\omega = 2 \pi {175 \over 3} = {350 \over 3} \pi = 366.519 {rad \over sec}$.

For the travel distance, you already know that the tire rotates at 3500 rpm, so in 10 minutes it will complete 35,000 rotations. Use the radius to calculate how much distance is traveled in one rotation: $2 \pi r = 0.425m \times 2\pi = {17 \over 20} \pi = 2.67 m$

And for 35,000 rotations: ${17 \over 20} \pi \times 35,000 = 29,750 \pi = 93462.38m$