Answer:
Part A) The angular speed of the wheels is [tex]23.53\frac{rad}{sec}[/tex]
Part B) Approximately 2,247 revolutions
Explanation:
Part A) What is the angular speed of the wheels?
we know that
The Angular speed is equal to divide the Linear speed by the radius
Let
s -----> the linear speed in m/sec
r -----> radius in m
w ----> angular speed in rad/sec
[tex]w=\frac{s}{r}[/tex]
we have
[tex]s=8\ m/sec\\r=34\ cm=34/100=0.34\ m[/tex]
substitute
[tex]w=\frac{8}{0.34}[/tex]
[tex]w=23.53\frac{rad}{sec}[/tex]
Part B) How many times does each wheel go round during a 10-minute ride? Â
we know that
As the wheel rotates one time, a point on the wheel rotates 2Ï€ radians.
Remember that
[tex]10\ minutes = 600\ seconds[/tex]
[tex]\theta = w * t = (\frac{8}{0.34}) * 600= \frac{4,800}{0.34}\ radians[/tex]
To find out the number of rotations divide by 2Ï€
[tex]\frac{\frac{4,800}{0.34}}{2\pi}=2,246.9[/tex]
Approximately 2,247 revolutions
