The wheels of the mountain bike have a diameter of 26 inches and are revolving at 60 radians per minute. What is the linear velocity of the mountain bike in feet per hour?

Question

I hate math and im struggling

Answer 1

For this problem, you are converting angular velocity to linear velocity.

Step 1) Write out what you know:

Angular velocity: ω = 60 radians / minute

Wheel diameter: d = 26 inches

Step 2) Use the angular velocity equation:

Angular velocity = linear velocity / radius

ω = v / r

We don't have the radius, but we can find it since we know the diameter:

Radius = diameter / 2

r = d / 2

r = 26 inches / 2

r = 13 inches

Now we can use the angular velocity equation:

ω = v / r (rewrite in terms of v)

v = ω * r

v = 60 radians / minute * 13 inches

v = 780 inches / minute (we can forget about radians since it is a dimensionless unit)

Step 3) Convert inches / minute into feet / hour:

We know that 12 inches = 1 foot, therefore:

780 inches / minute

= (780 / 12) feet / minute

= 65 feet / minute

It makes sense that this number is smaller because a foot is bigger than an inch.

We also know that 60 minutes = 1 hour, therefore:

65 feet / minute

= (65 * 60) feet / hour

= 3900 feet / hour

It makes sense that this number is bigger because you will go a further distance in 1 hour than you would in 1 minute.