A truck with 48-in.-diameter wheels is traveling at 45 mi/h.
(a) Find the angular speed of the wheels in rad/min.
rad/min
(b) How many revolutions per minute do the wheels make?
rev/min
45 mi/hr * 5280*12 in/mi /(2pi*48in/rev) * hr/60min * 2pi rad/rev = 3960 rev/min
rev/min = rad/min * rev/2pi rad, so divide 3960 by 2pi
Oops. Off by a factor of 2. I was using a radius of 48 in
Rats, I read it wrong also
radius should have been 24 , not 48
make the necessary adjustments in the above.
(time to go to bed)
To find the angular speed of the wheels in rad/min, we can use the formula:
Angular speed = Linear speed / Radius
First, let's convert the linear speed from mi/h to inches/min. Since there are 5280 feet in a mile and 12 inches in a foot, we can calculate the linear speed as follows:
Linear speed = 45 mi/h * (5280 ft/mi) * (12 in/ft) * (1/60 h/min)
Linear speed = 45 * 5280 * 12 / 60 in/min
Next, we need to find the radius of the wheels. The diameter is given as 48 inches, so the radius is half of that:
Radius = Diameter / 2 = 48 in / 2 = 24 in
Now we can substitute the values into the formula:
Angular speed = Linear speed / Radius
Angular speed = (45 * 5280 * 12 / 60) / 24
Angular speed = 211200 / 1440
Angular speed = 146.67 rad/min
Therefore, the angular speed of the wheels is 146.67 rad/min.
To find the number of revolutions per minute, we can use the formula:
Revolutions per minute = Angular speed / (2 * π)
Substituting the value of angular speed we found above:
Revolutions per minute = 146.67 / (2 * π)
Revolutions per minute ≈ 23.35 rev/min
Therefore, the wheels make approximately 23.35 revolutions per minute.
one rotation = 2π(48) = 96π inches
in 1 hour it goes 45 miles
= 45x5280x12 inches
= 2851200 inches
number of rotations per hour
= 2851200/(96π) = 9453.8.. rotations per hour
= 157.563 rpm
= 157.563x(2π) radians /min
= 990 radians/min