Question

A car is moving at a rate of 28 MPH, and the diameter of the wheel is about 2 1/3 feet. A) Find the number of revolutions per minute the wheels are moving B) Find the angular speed of the wheels in radians per minute

Answer 1

1. Know that: (1) in 28 miles, there are 147,840 ft because 28*5280, (2) radius is 7/6 because that is (2 1/3)/2, (3) C=2(pi)(7/6) or pi*7:3 2. To find revolutions per minute, you take 147,840 and divide it by the circumference to get revolutions per hour, which is about 20168.11439. Then, divide this by 60 to find revolutions per minute: 336.1352398 revolutions/min. 3. Then, to find the angular measure in radians you take the revolutions per minute and multiply it by 2pi.

Answer 2

The wheel makes 336.25 revolutions per minute, and its angular speed is 2111.67 rad/min.

Explanation:

Givens:

• 
  `v=28mph`
• 
  `d=2(1)/(3)ft=(7)/(3)ft`

When we talk about revolutions per minute, we refer to frequency, which is the inverse magnitude of period which is the time that takes doing one revolution. Another way to answer this question it's by transforming 28mph to rpm, but to do that we first have to find the angular speed.

`v=\omega r\\\omega =(28mph)/(2.21x10^(-4) mi)=12.67x10^(4)rad/hr`

But, we need to divide this angular speed by 60, to transform it to minutes.

`\omega = (12.67x10^(4))/(60) rad/min=2111.67 rad/min`

Which is the answer of the second questions.

Now, we transform this angular speed to rpm, to now how much revolutions per minutes there are:

We know that 1 revolution per minute is equal to 6.28 radians per minute, using this, we transform:

`2111.67 rad/min \ (1rpm)/(6.28 rad/min)=336.25 rpm`

Therefore, the wheel makes 336.25 revolutions per minute, and its angular speed is 2111.67 rad/min.