A wheel rolling at a constant speed has a radius of 15 inches and takes 30 seconds to roll 100 feet along the ground. What is its angular velocity? Use 3.14 for pie, and solve to two decimal places.
1 Rotation= 2(15)pi = 30pi this is the circumference in inches.
100ft=1200in
1200/30pi=12.74 amount of rotations it takes to finish the distance
12.74*2pi= 25.48pi this is the angle
now w=25.48pi/30, 30 being the amount of seconds it takes to complete 1200in
change it to degrees, degrees=radians*180/pi
d=25.48pi/30*180/pi
d=4586pi/30pi
d=152.88
152.88 degrees/second
The answer I got is 152.87 degrees/second.
152.87
I got 152.87
To find the angular velocity of the wheel, we need to know the relationship between the linear speed and the angular speed.
The linear speed is the distance traveled per unit of time along the circumference of the wheel, while the angular speed is the angle covered per unit of time by the wheel.
We can start by finding the linear speed of the wheel.
Given:
- Radius of the wheel, r = 15 inches
- Distance traveled by the wheel, d = 100 feet
We need to convert the distance from feet to inches, as the radius of the wheel is given in inches.
1 foot = 12 inches
So, the distance traveled by the wheel in inches is:
100 feet * 12 inches/foot = 1200 inches
The linear speed of the wheel is given by the formula:
Linear speed = Distance/Time
Substituting the values:
Linear speed = 1200 inches / 30 seconds = 40 inches/second
Now, let's find the angular speed.
The circumference of a circle is given by the formula:
Circumference = 2 * π * radius
Substituting the values:
Circumference = 2 * 3.14 * 15 inches = 94.2 inches
The angular speed is given by the formula:
Angular speed = Linear speed / Circumference
Substituting the values:
Angular speed = 40 inches/second / 94.2 inches = 0.425 radians/second
Therefore, the angular velocity of the wheel is 0.43 radians/second (rounded to two decimal places).
I rotation is 2(15)π = 30π
So, number of rotations in 100 feet = 100/(30π)
so angular velocity = 100/(30π) rotations / 30 second
= 100/(900π) *2π radians/second
= 2/9 radians/second
using 2 decimals, 2/9 = appr .22