Chapter 5: Circular Motion

What happens if you let go of the string?

If there's a centripetal force, the ball flies tangentially in the direction of velocity it had the moment it was released (no more inward force)

Frequency

number of revolutions per second (f)

Period

object revolving in a circle is the time required for one complete revolution (T) T = 1/f

Centripetal Acceleration

points towards center of circle (Ar) Ar = V2/r (magnitude of acceleration)

When a person swings a ball on the end of a string, what's the centripetal force?

the tension in the string is providing the centripetal acceleration pulling the ball inward, which causes the ball to exert an equal and opposite force on the string

What's the relationship between velocity and acceleration vectors?

they are perpendicular to each other at every point in the path

What is the tangential component of the acceleration Atan formula?

Atan = v/t

What is the velocity equation for circular motion?

v = distance/time = 2piR/T

What direction does the tangential acceleration always point to?

Always points in direction tangent to the circle and is in the direction of the motion (parallel to v, which is always tangent to the circle if speed is increasing

What direction is the velocity vector?

Always points in the direction of motion, which is tangential to the circle

What if the speed is decreasing?

Atan points antiparallel to v. Atan and Ar are always perpendicular to each other and their directions continually change as the object moves along its circular path

Equation for magnitude of the gravitational force

Fg = G((m1m2)/r2)

What is the equation for total net force in the radial direction?

Fr = mAr = m(v2/r)

What is the value of G?

G = 6.67E-11

Tetherball is played with a ball tied to a pole with a cord. After the ball is struck, it revolves around the pole. In what direction is the acceleration of the ball, and what force causes the acceleration, assuming constant speed?

If ball revolves in horizontal plane, acceleration points horizontally toward the center of the ball's circular path. The net force must point in direction of acceleration. The vertical component of the cord tension (Fty) balances the ball's weight, mg. The horizontal component of the cord tension, Tx, is the force that produces the centripetal acceleration towards the center.

What does it mean when the net force is not directed towards the center but is at an angle?

The force has two components. The component directed toward the center of the circle (Fr) gives rise to the centripetal acceleration (Ar) and keeps the object moving in a circle The component tangent to the circle, Ftan, cars to increase or decrease the speed, and thus gives rise to a component of the acceleration tangent to the circle, Atan

How do banked curves reduce the chance of skidding?

The normal force exerted by the banked road points towards the center, which reduces the reliance on friction Fnsina = m(v2/r)

What happens when you're sitting in a car that rounds a curve?

You feel like you're thrust outward towards the right side door BUT what's happening is that you tend to move in a straight line whereas the car has begun to follow a curved path. To make you go in the curved path, the seat (friction) or the door of the car exerts a force on you. The car also has a force exerted on it toward the center of the curve. On flat road, this force is supplied by friction between ties and pavement

What is the total vector acceleration?

a = Atan + Ar

What is the magnitude of a?

a = the square root of (a2tan + a2r)

What is the direction of total net force in a circular motion?

always pointing towards the center; net orcs is important because if there was no net force on an object, the object would be moving in a straight line direction is continuously changing so that it's always pointing towards the center

What is the radial acceleration formula?

arises from the change in direction of the velocity and has magnitude Ar = v2/r

Law of universal graviation

every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joing the two particles

What is the equation for g when considering gravity near Earth's surface?

g = G(Me/R2e)

Uniform Circular Motion

magnitude of velocity remains constant, but direction of velocity continuously changes around the circle object revolving in a circle is continuously accelerating (change in direction of velocity is acceleration)