# Two Problems Dealing With Circular Motion

• wetcarpet
In summary, the first conversation involves calculating the angle, in radians, that a wheel rotates in 1.0 s based on its rotational rate of 2.7 revolutions every 3.0 s. The correct answer is 5.65 radians, but the person is unsure due to their lack of knowledge in trigonometry. The second conversation involves determining the angle at which a highway curve should be banked to prevent a car traveling at 27.5 m/s from skidding sideways. This can be achieved by making the vertical components of the forces acting on the car add up to zero. The solution to this problem requires knowledge of centripetal acceleration and Newton's 2nd law.
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.

I get 5.65 too.

wetcarpet said:
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.

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

## 1. What is circular motion?

Circular motion is a type of motion where an object moves along a circular path, constantly changing its direction. This can occur when an object is moving in a circular orbit, rotating around a center point, or following a curved path.

## 2. What is centripetal force and how does it relate to circular motion?

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is necessary to maintain the object's curved path. Without centripetal force, the object would continue in a straight line.

## 3. How is angular velocity different from linear velocity?

Angular velocity refers to the rate of change of an object's angular position, while linear velocity refers to the rate of change of an object's linear position. This means that angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

## 4. Can an object in circular motion have a constant speed?

Yes, an object in circular motion can have a constant speed, but it must be constantly changing its direction. This means that its velocity is always tangent to the circular path and the object is not accelerating. However, the object's speed will remain constant as long as the radius of its circular path remains constant.

## 5. What is the difference between uniform circular motion and non-uniform circular motion?

In uniform circular motion, the speed of the object remains constant while its direction changes. In non-uniform circular motion, the speed of the object is changing, either increasing or decreasing, as it moves along the circular path. This is due to the presence of an external force, such as friction, acting on the object.

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