Question

B) The radius of a bicycle wheel is 50cm. In one-ninth of a second, it turns through 80°

about its center, which is fixed. How many kilometers does a point on the rim of the
wheel travel in one hour?​

Answer 1

A point on the rim of the bicycle wheel travels approximately 11,309.73 meters (or 11.31 kilometers) in one hour.

Step-by-step explanation:

To find the distance traveled by a point on the rim of the bicycle wheel in one hour, we need to determine the total number of revolutions made by the wheel in that time. First, we convert 1 hour to seconds, which is 3600 seconds. Next, we calculate the angular velocity of the wheel by using the formula:

angular velocity = angle rotated / time taken

Since the wheel rotates 80° in one-ninth of a second, we can calculate the angular velocity:

angular velocity = 80° / (1/9) = 720°/s

Now we convert the angular velocity to revolutions per second by dividing by 360° (one full rotation):

angular velocity = 720°/s / 360° = 2 revolutions per second

Finally, we multiply the revolutions per second by the circumference of the wheel (2πr) to find the distance traveled in one second:

distance traveled in one second = 2 revolutions/s * 2π(0.5m) = πm

Since there are 3600 seconds in an hour, we multiply the distance traveled in one second by 3600 to find the total distance traveled in one hour:

total distance traveled in one hour = πm * 3600 = 3600πm = 11309.73m

Therefore, a point on the rim of the bicycle wheel travels approximately 11,309.73 meters (or 11.31 kilometers) in one hour.

Answer 2

Given data:

Radius r = 50cm

Time taken by the wheel to turn 80 degree = 1/9 seconds

= > In one second, wheel turns 720 degree

We know that one revolution is 360 degree

Therefore in one second, it takes 2 revolutions

In one hour i.e. 3600 seconds, it takes 7200 revolutions

Distance travelled by the wheel in one revolution is equal to the circumference of the wheel.

Distance travelled in one revolution = 2 π r = 2 π x 50 = 100 π cm

Distance travelled in one hour i.e. for 7200 revolution = 720000 π cm

So, distance travelled by the point on the rim of the wheel in an hour = 7.2 π km = 22.6 km

Step-by-step explanation: