A truck with 36-in.-diameter wheels is traveling at 55 mi/h.
Find the angular speed of the wheels in rad/min, *hint convert miles to inches & hours to minutes
How many revolutions per minute do the wheels make?
• This question is 2 parts. I can't remember the formula for linear and angular velocity. I've always been a bit confided with problems like this. Could someone please explain to me how to solve this? Thank you!!!
circumference of tire = pi D = 36 pi =113 inches/revolution
55 mi/h (1 h/60min)(5280ft/mi)(12 in/ft)
= 58,080 inches/min
58080 inches/min (1 rev/113 in) = 514 rev/min
514 rev/min ( 2 pi radians/rev) = 3229 radians/min
Well, well, well, seems like we've got a good old wheel conundrum here!
Let's start by finding the linear velocity, which is basically the speed of an object moving in a straight line. To find that, we need to convert the 55 miles per hour to inches per minute, as the hint suggests.
Now, there are 5280 feet in a mile and 12 inches in a foot, right? So, we have:
55 miles/hour * 5280 feet/mile * 12 inches/foot * 1 hour/60 minutes
Doing the math here:
55 * 5280 * 12 / 60 = 633600 inches/minute
Okay, so we've got the linear velocity sorted out. Now let's move on to angular velocity, which is the rate at which an object rotates or spins.
To find the angular speed of the wheels in rad/min, we need to convert the linear velocity to angular velocity. The formula to do that is:
Angular velocity = Linear velocity / Radius of the wheel
In this case, the radius of the wheel is half of the diameter, which is 36 inches divided by 2. So, we have:
Angular velocity = 633600 inches/minute / (36 inches/2) = 35200 revolutions/minute.
There you have it! The wheels make approximately 35200 revolutions per minute.
Keep on rolling with those questions, and remember: the world is your circus!
To find the angular speed of the wheels in rad/min, we need to convert the linear speed of the truck into angular speed.
1. First, let's convert the diameter of the wheels from inches to feet.
Since 1 foot = 12 inches, the diameter in feet would be 36 inches / 12 = 3 feet.
2. Now, we can convert the speed of the truck from miles per hour to feet per minute.
There are 5280 feet in a mile, so the speed in feet per minute would be 55 miles/hour * 5280 feet/mile / 60 minutes/hour = 4840 feet/minute.
3. Next, let's find the circumference of the wheels.
The circumference is given by the formula: circumference = π * diameter.
So, the circumference of the wheels would be 3.14 * 3 feet = 9.42 feet.
4. Now, we can find the distance the wheels travel in one minute by multiplying the circumference by the number of revolutions per minute.
Let's denote the number of revolutions per minute as 'r'.
The distance traveled in one minute would be 9.42 feet/rev * r rev/min = 9.42r feet/min.
5. We know that the distance traveled in one minute is also equal to the linear speed of the truck in feet per minute (4840 feet/minute):
9.42r feet/min = 4840 feet/min.
Now, we can solve for 'r' by dividing both sides of the equation by 9.42:
r = 4840 feet/min / 9.42 feet/rev ≈ 515.42 rev/min.
So, the wheels make approximately 515.42 revolutions per minute.
To find the angular speed of the wheels in rad/min, we can multiply the number of revolutions per minute by 2π (since there are 2π radians in one revolution):
Angular speed = 515.42 rev/min * 2π rad/rev ≈ 3241.06 rad/min.
Therefore, the angular speed of the wheels is approximately 3241.06 rad/min.
To solve this problem, we need to use the formulas for linear velocity and angular velocity.
Linear velocity is the rate at which an object moves along a straight line, and it is given by the formula:
Linear velocity = Distance traveled / Time taken
In this case, the distance traveled is the circumference of the wheel, which can be found using the formula:
Circumference = π * diameter
The time taken can be converted from hours to minutes by multiplying by 60.
To find the angular velocity, we use the formula:
Angular velocity = Linear velocity / Radius
The radius of the wheel is equal to half of its diameter.
Now let's calculate the values step by step:
1. Convert miles to inches:
Since there are 5280 feet in a mile and 12 inches in a foot, we can calculate the number of inches in a mile as:
Inches in a mile = 5280 * 12
2. Convert hours to minutes:
Since there are 60 minutes in an hour, multiplying the given speed of 55 mi/h by 60 will give us the speed in mi/min:
Speed in mi/min = 55 * 60
3. Calculate circumference:
Using the formula for the circumference of a wheel, we can find its value:
Circumference = π * diameter
Circumference = π * 36 inches
4. Calculate linear velocity:
Using the formula for linear velocity, we can calculate its value:
Linear velocity = Distance traveled / Time taken
Linear velocity = Circumference * Speed in mi/min
5. Calculate angular velocity:
Using the formula for angular velocity, we can calculate its value:
Angular velocity = Linear velocity / Radius
Angular velocity = Linear velocity / (36 inches / 2)
6. Convert angular velocity to rad/min:
Since there are 2π radians in a full revolution, to convert angular velocity to rad/min, we can multiply it by (2π) / (1 min).
Finally, to calculate the number of revolutions per minute:
Revolutions per minute = Angular velocity / (2π)
By following these steps and plugging in the appropriate values, you should be able to solve the problem.