Physics: Circular Motion and the Law of Gravity

Angular Displacement

the angle in radians through which a point of line rotates around a center or axis of rotation. theta=x/r

circular motion

movement of an object along the circumference of a circle or rotation along a circular arc. Angle in center of the circle

angular velocity

rate of change of angular displacement. w=(theta f-theta i)/(tf-ti)

angular acceleration

ratio of the change in angular velocity to the time it takes for the object to undergo the change. alpha=(wf-wi)/(tf-ti)

relationship between angular displacement and linear displacement

x=theta*r. angular displacement is the change in angle from initial position to final position while linear displacement is the change in distance from initial to final position

relationship between angular velocity and linear speed

v=wr. linear speed is directly proportional to angular velocity (w) through the radius (r) of the circular path

relationship between angular acceleration and linear acceleration

a=alpha*r. linear acceleration(a) is directly proportional to angular acceleration(alpha), and inversely proportional to distance from the axis of rotation.

rotation and revolution

rotation is spinning motion of an object around its own axis while rotation is the movement of an object around another object typically in an elliptical or circular path. ex. the earth’s rotation creates day an night, while it’s revolution around the sun creates a year.

radian

when an object moves in a circle, the arc distance is equal to the radius of the circle, then the angular displacement is called 1 radian. x=r, theta=1 radian

centripetal acceleration

an object traveling in a circle, even though it moves with a constant speed, will have an acceleration. ac=w²r

Newton’s Gravitational Law

Any 2 objects either attract or repel each other.

F=G(m1m2)/r²

Attract with force directly proportional to the product of masses, inversely proportional to the square of the distance between radius’

Escape Velocity

The Speed needed for an object to soar off into space and not return. Changes based on the planets.

Vesc=11.2 km/s for the earth

Vesc= square root of (2GM/R)

drawing is spaceship leaving planet

Kepler’s First Law

All the planets move in elliptical orbits with the Sun at one focus

diagram has sun and planet

Kepler’s Second Law

A line drawn from the Sun to any planet will sweep out equal areas in equal times

diagram has sun and big circle showing the sun’s light from january to march and from may to july.

^OAB = ^OCD

Kepler’s Third Law

The square of the orbital period of any planet is proportional to the cube of the average distance from the Sun to the planet

T= orbital time period

r= average distance

k= Kepler’s constant

T²=kr³

convert from degrees to radians

multiply by pi/180

convert from radians to degrees

multiply by 180/pi

how to find force between the sun and a planet

F=6.673×10^-11 ((1.991×10^30)(m2))/(r²)