Physics M03

circular motion

any motion in which an object is moving along a curved path

tangential (or linear) speed

the linear speed of something moving along a circular path with a direction of motion tangent to the circumference of the circle (m/s or km/h)

rotational (or angular) speed

number of rotations (or revolutions) per unit of time (rpm)

what is the relationship between tangential speed and rotational speed?

tangential speed is directly proportional to rotational speed at any fixed distance from the axis of rotation

what is the relationship between tangential speed and distance from the axis?

tangential speed is directly proportional to distance from the axis for any given rotational speed (like how the edge of a merry-go-round is faster than the inner part)

tangential speed relationships symbolic expression

v (tangential speed) ~ r(radial distance) x w(rotational speed)

rotation

when an object turns about an internal axis

revolution

an object moving about an external axis

tangential acceleration

when tangential speed undergoes change, indicating an acceleration parallel to tangential motion

centripetal acceleration

acceleration toward the center of a curved or circular path

centripetal force

any force from a fixed center that causes a body to move in a circular path as a result from a pull

what force is exerted on a centripetal force?

the only force exerted is directed toward the center of circular motion; there is no outward force acting

centripetal force equation

m = mass; v=tangential speed; r=radius of curvature

centrifugal force

a fictitious force that acts outward on a body moving around a center, arising from the body's inertia.

simulated gravity

a centrifugal force that feels like gravity

rotational inertia

the property of an object to resist changes in its rotational state of motion dependent on mass

rotational inertia and mass

the greater the distance between an object's mass concentration and the axis, the greater the rotational inertia

torque

a force that causes rotation

lever arm

the perpendicular distance from the axis of rotation to the point where force is exerted

torque (t) equation

lever arm x force

mechanical equilibrium and torque

net torque on a body or on a system must be zero for mechanical equilibrium

center of mass

the average position of all the mass that makes up an object. Can be where no mass exists

center mass and stabilization

to be stable, the center of mass has to be over the area of support

torques and center of mass

there is evidence of equal and opposite torques

center of gravity

the average position of the weight distribution

center of gravity in a uniform object

at its midpoint

finding the center of gravity of an irregularly shaped object

suspend it from a point and use a plumb line to draw a vertical line on the object. Repeat this from a second point of suspension. The intersection of these two lines is the object's center of gravity

center of gravity and equilibrium

an object is in stable equilibrium when a line drawn straight down from the center of gravity of an object falls inside the base of the object

angular momentum

Product of rotational inertia and rotational velocity ( ___ = mvr)

a rule of angular momentum

an object or system of objects will maintain its angular momentum unless acted upon by an external net torque

conservation of angular momentum

if no external net torque acts on a rotating system, the angular momentum of that system remains constant

newton's law of universal gravitation

for any pair of objects, each particle attracts the other object with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between their centers of masses, where F is force, m is mass, d is distance, and G is the universal gravitational constant

gravity and distance relationship

Greater distance results in weaker gravitational force.

inverse-square law

the intensity of radiation is inversely proportional to the square of the distance from the source of radiation

weightlessness

an object's apparent weight of zero that results when there are no contact forces pushing up on the object

Ocean tides are caused by

The differences in the gravitational pull of the Moon on opposite sides of Earth

spring tides

a tide just after a new or full moon, when there is the greatest difference between high and low water.

neap tides

tides that occur when the moon is halfway between a new Moon and a full Moon, in either direction. The high tides are lower than average and low tides are not as low as average low tides

why don't tides occur in ponds or fluids in bodies?

because no part of the pond or fluids in the body are significantly closer to the Moon or Sun than any other part

gravitational fields

a force field that exists in the space around every mass or group of masses; measured in newtons per kilogram

Einstein’s Theory of Gravity

the warping of space by masses affects the motion of objects

black holes

regions of space where gravity is so strong that nothing, not even light, can escape from them.

perturbation

the alteration (wobble) of a system caused by a disturbance or the influence of external forces.

projectile motion

the motion of an object thrown into the air, subject to gravitational acceleration, following a curved trajectory.

horizontal velocity and vertical velocity in projectile motion

are the components of the object's motion, where horizontal velocity remains constant and vertical velocity changes due to gravity.

satellites

are objects that orbit a planet or celestial body, typically following an elliptical path due to gravitational forces.

circular satellite orbits

refer to the motion of satellites traveling along a circular path at a constant altitude, maintaining a constant speed while being influenced by gravitational pull.