# A bicycle wheel of radius 10cm is turning at a rate of 5 revolutions per minute. Calculate the distance moved by a point on the rim in 2 seconds.

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When the wheel rotates one revolution the point of the rim will travel a distance which is equal to circumference of the wheel circle.

Distance travel for one revolution `= 2pir`

Distance travel for one revolution `= 2pixx10 = 20picm`

The wheel rotates 5 revolutions per minute. So the distance travel by the point will be `20pixx5 = 100pi` .

For one minute(60 seconds) the point travels 100picm distance.

So distance travelled in 2 seconds `= 100pixx2/60 = 10.47cm`

*So the answer is 10.47cm.*

*Note*

*Here we have to assume that the wheel rotates at a constant speed.*

To find the distance a point on the rim will move in 2 seconds, we must first find the circumference of the wheel. To do this we use the formula C=2pi r.

The circumference of the wheel = 2x3.14x10cm.=62.8cm.

The wheel is moving at 5 revelutions per minute, to find how far the wheel revolves in 1 second, we need to divide 5 by 60. The wheel is making 5/60 or 1/12 of a revolution per second. The wheel will travel 62.8 x 1/12 cm per second or 5.23333 cm/ second.

Since we are traveling for 2 seconds, we need to multiply 5.23333x2 which gives us 10.4666 or 10.47 cm.