I need help with solving these word problems.

Marion rides her racing bicycle @ speed of 8 m/s. Bicycle wheels have a radius of 34 cm. What is the angular speed of wheels? How many times does each wheel go around during a 10-min race?

A car tire has radius of 33cm. Tire turns a total of 10,250 radians during trip to store. How many meters did car travel?

r = 0.34 m

omega r = 8 m/s
omega = 8/.34 radians/second

10 min = 600 s
600 * 8/.34 = total radians in 10 minutes
divide that by 2 pi radians per revolution

r = 0.33 m
angle in radians * r = distance travelled
10,250 *.33 = answer

tangenial speed=angularspeed*radius

tangential speed is given, as is radius.

for the second, revolutions/2PI=angularspeed*time

Is the answer for the 1st question ...23.5 rad/ sec?

Is the answer for the 2nd question...66 times?

Is the answer for the 3rd question...3382.5 meters?

How do you turn 30 degrees to radians?

To solve the first word problem, we need to find the angular speed of the wheels and the number of times each wheel goes around during a 10-minute race.

1. Angular speed of the wheels:
The angular speed (ω) is the rate at which an object rotates or turns. It is usually measured in radians per second (rad/s).

To find the angular speed of the wheels, we need to first calculate the circumference of the wheels using the formula:
Circumference = 2π * radius

Given that the radius of the wheels is 34 cm, we can plug it into the formula:
Circumference = 2π * 34 cm

Once we have the circumference, we can find the angular speed by dividing Marion's speed (8 m/s) by the circumference:
Angular speed = Speed / Circumference

2. Number of times each wheel goes around:
To find the number of times each wheel goes around during a 10-minute race, we need to calculate the total angle covered by the wheels.

The total angle covered by the wheels is calculated by multiplying the angular speed by the time:
Total angle = Angular speed * Time

Since the time given is 10 minutes, we need to convert it to seconds before calculating the total angle:
Total angle = Angular speed * (10 minutes * 60 seconds/minute)

Now, we can find the number of times each wheel goes around by dividing the total angle by 2π radians (since one full revolution is equal to 2π radians):
Number of times each wheel goes around = Total angle / (2π)

To solve the second word problem, we need to find the distance traveled by the car given the number of radians the tire turned.

1. Distance traveled by the car:
The distance traveled (d) can be calculated using the formula:
Distance = Arc Length = Radius * Angle

In this case, the radius of the car tire is given as 33 cm, and the angle turned by the tire is given as 10,250 radians. We can plug these values into the formula:
Distance = 33 cm * 10,250 radians

However, to get the distance in meters, we need to convert the radius from centimeters to meters:
Distance = (33 cm / 100) m * 10,250 radians

Now you have the steps to solve both word problems. Let me know if you need any further assistance.