A friend needs help with the following physics problems and we don't know how to do it:?

Question

A spot of paint on a bicycle tire moves in a circular path of radius 0.29 m. When the spot has traveled a linear distance of 1.30 m, through what angle has the tire rotated? Give your answer in radians.

On a certain game show, contestants spin a wheel when it is their turn. One contestant gives the wheel an initial angular speed of 3.10 rad/s. It then rotates through one-and-one-quarter revolutions and comes to rest on the BANKRUPT space. Through what angle has the wheel turned when its angular speed is 1.50 rad/s?

Answer 1

Question 1
r*theta = 1.3m
theta=1.3/.29=4.483 radian

Question 2
3.1 r/s is to 1.24 turns as 1.5 r/s is to x turns
or
0.6 turns

Answer 2

part 1

2 pi radians = 360 degrees
2pi radius = circumference of the wheel
divide the circ. into the 1.30 meters to get revolutions then multiply by 2 pi to =radians

Answer 3

well 4 the top one, i know you probably just want the answer but anyway, you first find the cicumference of the tire: ((0.29^2) * pi 3.141) then you put that answer over 1.3m (circum. of tire/ 1.3)=X over 360 .... cross multiply .....circum.oftire*360= X over 1.3
the answer is the angle the tirehas rotated

Answer 4

archlength=radius x angle in radian......
1.3/0.29= answer