Question

A three inch diameter pulley on an electric motor that runs at 1800

revolutions per minute is connected by a belt to a six inch
diameter pullley on a saw arbor.
angular speed = central angle/time, arc length = (central
angle)(radius)

a. Find the angular speed (in radians per minute) of each. ( 3 in
and 6 in pully)

b. find the revolutions per minute of the saw.

Answer 1

a. The angular speed of the 3 inch pulley is 3600π radians/min and the angular speed of the 6 inch pulley is 7200π radians/min. b. The revolutions per minute of the saw is 900.

Step-by-step explanation:

a. To find the angular speed in radians per minute, we need to convert the revolutions per minute to radians per minute. Since 1 revolution is equal to 2π radians, we can calculate the angular speed of the 3 inch pulley as follows:

Angular speed = (Revolutions per minute) x (2π radians per revolution)

Angular speed = (1800 rev/min) x (2π radians/rev) = 3600π radians/min

Similarly, for the 6 inch pulley:

Angular speed = (Revolutions per minute) x (2π radians per revolution)

Angular speed = (1800 rev/min) x (2π radians/rev) = 7200π radians/min

b. To find the revolutions per minute of the saw, we need to use the ratio of the diameters of the two pulleys. Since the diameter of the 6 inch pulley is twice the diameter of the 3 inch pulley, the revolutions per minute of the saw will be half of the revolutions per minute of the motor. Therefore, the revolutions per minute of the saw is 900.

Answer 2

a) 3 inch pulley: 11,309.7 radians/min

6) 6 inch pulley: 5654.7 radians/min

b) 900 RPM (revolutions per minute)

Step-by-step explanation:

Hi!

When a pulley wirh radius R rotantes an angle θ, the arc length travelled by a point on its rim is Rθ. Then the tangential speed V is related to angular speed ω as:

`V=R\omega`

When you connect two pulleys with a belt, if the belt doesn't slip, each point of the belt has the same speed as each point in the rim of both pulleys: Then, both pulleys have the same tangential speed:

`\omega_1 R_1 = \omega_2 R_2\\`

`\omega_2 = \omega_1 (R_1)/(R_2) =1800RPM* (3)/(6)= 900RPM`

We need to convert RPM to radias per minute. One revolution is 2π radians, then:

`\omega_1 = 1800*2\pi (radians)/(min) = 11,309.7(radians)/(min)`

`\omega_2 = 5654.7 (radians)/(min)`

The saw rotates with the same angular speed as the 6 inch pulley: 900RPM