im cconfused pre cal assignment

Question

A truck with 46-in.-diameter wheels is traveling at 50 mi/h.

Find the angular speed of the wheels in rad/min, *hint convert miles to inches & hours to minutes: ____   rad/min

How many revolutions per minute do the wheels make?____    rpm

Answer 1

LinearVelocity = Radius* Angular velocity

Linear velocity = 50 mi/hr

Radius = 23 inch

50 mile/hr = 50* 63360 inch /hr= = 50 * 63360/60 inch /min

Angular Velocity = Linear Velocity /radius 50*63360/(60*23) rad/min

Answer 2

Let's start by using the hint that the problem statement gives us, and convert miles to inches and hours to minutes.

There are 63360 inches in 1 mile and 60 minutes in 1 hour

To convert miles/hour to inches/min, we can multiply by 63360 and then divide by 60.

50 x 63360 / 60 = 52800

So, the wheels are traveling at 52800 inches/min

Now we can notice that since the wheels have a 46 inch diameter, the radius is 23, so we can calculate the circumference using the following formula,

Circumference = 2πr = 2π(23) = 46π inches

Next, we can find the number of revolutions per minute by dividing the speed by the circumference,

46π / 52800 ≈ 365.38 (revolutions / min)

Lastly, we need to convert the revolutions per min to radians / min

Since we know that a full 360 degree revolution is 2π radians, we just need to multiply by 2π.

365.38 x 2π ≈ 2295.65 radians / min