A pulley with a radius of 8 inches rotates three times every five seconds. Find the
angular velocity of the pulley in radians/sec (round to the nearest hundredth). Find the
linear velocity to the nearst ft/hr.
angular speed=3rev/5sec*2pirad/rev=6PI/3
=2PI/sec
linear velocity? Surely you mean tangential velocity, tangential velocity=angularvelcity*radius
To find the angular velocity of the pulley in radians/sec, we can use the formula:
Angular Velocity (in radians/sec) = 2π * (Number of rotations) / (Time taken in seconds)
In this case, the pulley rotates three times every five seconds. So, the number of rotations is 3 and the time taken is 5 seconds.
Angular Velocity = 2π * 3 / 5
Angular Velocity ≈ 3.77 radians/sec (rounded to the nearest hundredth)
To find the linear velocity in ft/hr, we need to know the circumference of the pulley. The circumference (C) of a circle can be calculated using the formula:
Circumference = 2π * Radius
In this case, the radius of the pulley is given as 8 inches.
Circumference = 2π * 8 inches
To convert inches to feet, we divide it by 12 since there are 12 inches in a foot.
Circumference = (2π * 8) / 12 feet
Now, since the pulley completes one rotation in 2π radians, the distance travelled along the circumference is equal to the circumference itself.
So, the linear velocity (V) can be calculated using the formula:
Linear Velocity (in ft/sec) = Circumference * Angular Velocity
Since we need the result in ft/hr, we can convert ft/sec to ft/hr by multiplying by 60 (minutes) and then by 60 (hours).
Linear Velocity (in ft/hr) = Linear Velocity (in ft/sec) * 60 * 60
Substituting the values into the formula:
Linear Velocity (in ft/hr) = [(2π * 8) / 12] * 3.77 * 60 * 60
Linear Velocity ≈ 1197.94 ft/hr (rounded to the nearest hundredth)