Wheels A and B are connected by a belt, Wheels B and C are connected
by an axle, and Wheels C and D are connected by a belt.
Suppose Wheel A has radius 7 cm, Wheel B has radius 4 cm, Wheel C has radius 1.5 cm,
and Wheel D has radius 10 cm. If Wheel A makes 4 full rotations per minute, what is the
angular speed of Wheel D? Express your answer in radians per second.
omega B= (4/7) omega A
omega C = omega B = = (4/7) omega A
omega D = (1.5/10) omega C = (1.5/10)(4/7) omega A
so
if omega A = 4
omega D = (1.5/10)(4/7) (4) = 0.343 rev/min
0.343 rev/min * 2 pi radians/ rev * 1 min/ 60 s = 0.036 radians/sec
thank you so much!
You are welcome.
To find the angular speed of Wheel D, we need to find the relationship between the angular speeds of the wheels.
First, let's find the angular speed of Wheel B. Since Wheel A makes 4 full rotations per minute, we know that its angular speed is:
Angular speed of Wheel A = 4 rotations/minute
To convert this to radians per second, we need to multiply by 2π (since there are 2π radians in one full rotation) and divide by 60 (to convert minutes to seconds):
Angular speed of Wheel A = 4 rotations/minute * 2π radians/rotation / 60 seconds/minute
Simplifying this expression, we have:
Angular speed of Wheel A = 4 * 2π / 60 radians/second
= (8π / 60) radians/second
= (4π / 30) radians/second
Now, let's find the angular speed of Wheel B. The belt connecting Wheel A and Wheel B ensures that they have the same angular speed. Therefore, the angular speed of Wheel B is the same as that of Wheel A:
Angular speed of Wheel B = (4π / 30) radians/second
Next, let's find the angular speed of Wheel C. Wheel C is connected to Wheel B by an axle, which means they rotate at the same angular speed. Therefore, the angular speed of Wheel C is also (4π / 30) radians/second.
Finally, let's find the angular speed of Wheel D. The belt connecting Wheel C and Wheel D ensures that they have the same angular speed. Therefore, the angular speed of Wheel D is the same as that of Wheel C:
Angular speed of Wheel D = (4π / 30) radians/second
So, the angular speed of Wheel D is (4π / 30) radians per second.