As long as the bead stays on the surface ##\dot R## = 0. That should simplify things for you.MathDestructor said:
Please show the revised velocity and acceleration in view of my comments in post #4. You cannot proceed to the second part unless you get the first part right. If you have to post pictures (a practice we discourage) at least make sure they are right side up.MathDestructor said:
You need to write a vector equation. How many different forces act on the bead when it is on the surface at angle φ? Write their vector sum in unit vector notation and set it equal to ##m\vec a## in unit vector notation. Your expressions for the velocity and acceleration are correct.MathDestructor said:
I don't know what that means, or how to do that.kuruman said:
Sorry, it is against forum rules. Do your best. Identify the forces that act on the bead, draw a free body diagram and use it to write each force in unit vector notation.MathDestructor said:
Polar coordinates are a type of coordinate system that is used to describe the position of a point in a plane. They consist of a distance from the origin (known as the radius) and an angle from a reference direction (usually the positive x-axis). In mechanics problems, polar coordinates are used to describe the motion of objects in a circular or curved path.
To convert from polar to Cartesian coordinates, you can use the following equations: x = r * cos(θ) and y = r * sin(θ), where r is the radius and θ is the angle. To convert from Cartesian to polar coordinates, you can use the equations: r = √(x^2 + y^2) and θ = tan^-1(y/x).
Polar coordinates are commonly used in mechanics to describe the motion of objects in circular or rotational motion, such as the swinging of a pendulum, the rotation of a wheel, or the orbit of a planet around a sun. They are also used in problems involving forces acting at an angle, such as in projectile motion.
To solve mechanics problems using polar coordinates, you first need to identify the variables involved, such as the radius, angle, and velocity. Then, you can use equations such as Newton's second law or conservation of energy to analyze the motion of the object. It is important to keep track of the direction of the forces and velocities, as they are represented by angles in polar coordinates.
One advantage of using polar coordinates in mechanics is that they are well-suited for describing circular or rotational motion. They also make it easier to analyze forces and velocities that are acting at an angle. Additionally, polar coordinates can simplify equations and calculations in certain mechanics problems, making them more efficient to solve.