When a wheel is rotated through an angle of 35 degrees, a point on the circumference travels through an arc length of 2.5 m. When the wheel is rotated through angles of 35 rad and 35 rev, the same point travels through arc lengths of 143 m and 9.0 X 10^2 m, respectively. What is the radius of the wheel?

Question

I know that the radius is the change in arc length divided by the change in the angle in radians, but I don't understand the second sentence (the 35 rev part).

Answer 1

I think the first sentence is extra information. Here's my work:

Change in arc/change in radians = 757 / 184.9 = 4.09 meters

To get the change in arc, I did:

900m - 143m = 757 m

To get the change in radians, I did:

70pi radians - 35 radians = 184.9 radians

Is my answer of 4.09 m for the radius correct?

Answer 2

The first sentence is all you need.

arc distance=radius*angleinRadians
2.5=radius(35deg*PIrad/180deg)
radius=4.09 m

Answer 3

thanks! :D

Answer 4

thanks! :D
though some more explanation would be appreciated for example why (35*PIrad/180deg), because you are converting degrees into radians