Angular displacement of rotating wheel and banking angle for a highway curve

[wetcarpet]

1) A wheel is rotating at a rate of 2.7 revolutions every 3.0 s. Through what angle, in radians, does the wheel rotate in 1.0 s?

I tried to solve this problem by:
{a} 360 x 2.7 = 972
{b} 972 / 3 = 324
{c} 364 / (180 / Pi) = 5.65

Yet, 5.65 is not the answer. The rust coated around the section of my brain labeled 'Trigonometry' is probably the culprit here.

2) A highway curve has a radius of 127 m. At what angle should the road be banked so that a car traveling at 27.5 m/s has no tendency to skid sideways on the road? [Hint: No tendency to skid means the frictional force is zero.]

I have no train of logic on this problem because I'm utterly spellbound. I feel as if perhaps I'm minus an essential formula, though.

Any suggestions or advice would be a godsend.

 

[quasar987]

I get 5.65 too.

 

[Doc Al]

Yet, 5.65 is not the answer.

I think it is.

2) A highway curve has a radius of 127 m. At what angle should the road be banked so that a car traveling at 27.5 m/s has no tendency to skid sideways on the road? [Hint: No tendency to skid means the frictional force is zero.]

No tendency to skid means that a frictional force is not required to keep the car from sliding.

The car is centripetally accelerating. Consider Newton's 2nd law. (What forces act on the car?) Hint: The vertical components of the forces must add to zero.

 

[whozum]

You're quoting two different numbers for the number of degrees per second, pick one!