Uniform Circular Motion

when asked for net force in a centripetal acceleration problem

F net = mv^2 / r

A housefly of mass m is sitting on the horizontal blade of a ceiling fan and has a tangential speed of v as the fan spins. The coefficient of static friction between the fly and the blade is μs and the acceleration due to gravity is g. What is the maximum distance the fly can be from the point of rotation of the fan?

F(net) = F(static) Fc = F static mv^2 / r = Mu mg solve for radius

Centripetal

(means center seeking) word used to describe the acceleration of an object undergoing UCM (ac)

A car is traveling around a banked curve on a road, meaning the road is not flat, but at an angle with the horizontal. The car hits a patch of ice (static friction force is zero) on the road and slides at constant velocity around the curve. Is it possible for the car to slide around the curve and stay on the road?

In this situation can only depend on the normal force and the centripetal force and not static - therefore if the road is angled (steep) enough it will not slide bc the normal force can provide centripetal force.

when asked for tension in a centripetal acceleration problem

T = mv^2 / r

magnitude of centripetal acceleration

ac= v^2/r

when asking for tension of a rope holding a bar

add up the weights of the forces and that is the tension as that is what can hold up those forces to remain in static equilibrium

center of turning

all systems that can spin or rotate have this. This is the point that does not move while the remainder of the object is rotating, effectively becoming the center of the circle. also known as the pivot point and or fulcrum

if a question asks for the net force and a object is going in a circle its asking for

centripetal force Fc = mv^2 / r

tangential acceleration

changes the speed

Centripetal acceleration

does not change the speed, only changes the direction

if an object is accelerating then it must be

feeling a force

determining if a car will make a turn on a race track:

find net force (centripetal force) find static force (Mus (mg)) as long as speed is below the static max it will make the turn

Translational equilibrium

if the forces cancel; if Fnet = 0; then translational acceleration is zero no net torque no net force

rotational equilibrium

if the the torques cancel; if T net = 0, then the rotational acceleration (alpha) is zero

fc =

mac mv^2 / r

Torque

measure of a force's effectiveness at making an object spin or rotate (more precisely, it's the measure of a force's effectiveness at making an object accelerate rotationally)

if an object is initially at rest, and then it starts to spin

something must have exerted a torque

On a flat road the thing that keeps the car down (and also during flat road turns)

static friction and centripetal force

On a curved road the thing that keeps the car down is

static friction, centripetal force, and normal force

equation for torque

t = rfsintheta

velocity is always

tangent to the circle

For an object that travels in a circular path at constant speed:

the acceleration is not zero and is always directed toward the center of the path.

The bucket is traveling in a circle, so the net force is the same as

the centripetal force and is acting towards the center of the circle. By definition, the centripetal force is the net force acting towards the center of the circle

where is the pivot on a revolving door

the door hinge

With the rod in equilibrium, the net force upward (the tension T in the supporting string) must balance

the net force downward (the total weight of the hanging objects),

A uniform bar is lying on a flat table. In addition to its weight and the normal force exerted by the table (which exactly balances the bar's weight), exactly two other forces, F1 and F2, act on the rod. If the net force acting on the rod is zero, then:

the net torque will be zero if F1 and F2 are applied at the same point on the rod.

In order to make an objects center of mass accelerate we need a

torque

Static equilibrium

velocity happens to be at zero (no motion

center of mass equation

xcm = m1x1 + m2x2..../M1 + m2 | x is postion, m is mass M is total mass of the system

Equilibrium

zero acceleration. this does not mean zero velocity. As long as velocity of system remains constant (no change in speed or direction) - then we can say system in equilibrium.

uniform circular motion

-speed is constant - velocity is not constant because the direction of velocity is always changing -in order to produce acceleration there must be a force towards the center

centripetal force

net force directed toward the center that acts on an object to make it execute uniform circular motion

During uniform circular motion

non zero acceleration due to a changing velocity even if the speed is constant

velocity and centripetal acceleration are always

perpendicular

acceleration of a circle always

points towards the center of circle

An object is moving in a circle at constant speed. Its acceleration vector must be directed:

radially toward the center of the circle