Question

Wheel a of radius ra =10 cm is coupled by belt b to wheel c of radius rc =25 cm. the angular speed of the wheel a is increased from rest to constant rate of 1.6 rad/s 2 . find the time needed for wheel c to reach an angular speed of 100 rev/min, assuming the belt does not slip. (hint: if the belt does not slip, the linear speeds at the two rims must be equal)

Answer 1

The time needed for wheel C to reach an angular speed of 100 rev/min, assuming the belt does not slip, is 6.21 seconds.

Step-by-step explanation:

To find the time needed for wheel c to reach an angular speed of 100 rev/min, we can use the concept of angular velocity. Since the linear speeds at the two rims must be equal, we can equate the angular velocities of wheels A and C. The angular velocity of wheel A is given as 1.6 rad/s², and we can calculate the angular velocity of wheel C using the formula:

ωc = ωa * (ra/rc)

Substituting the values, we get:
ωc = 1.6 * (10/25) = 0.64 rad/s

Now, we can calculate the time needed for wheel C to reach an angular speed of 100 rev/min (approximately 10.47 rad/s) using the formula:

t = Δω / α

Substituting the values, we get:
t = (10.47 - 0.64) / (1.6) = 6.21 seconds