Physics U11: Circular Motion and Gravity

What is centripetal force?

Any object moving in a circle undergoes an acceleration that is directed toward the center of the circle - centripetal "towards the center." The force directed toward a fixed center that cause an object to follow a circular path is the centripetal force. *It forces you into a circular path. If it ceased to act, you'd move in a straight line, in accord with the law of inertia."

What are the different ways we can think of speed in circular motion?

We can think of it as circular/angular/rotational speed or we can think of it as linear/tangential speed.

What is rotation?

When an object turns about an *internal* axis - located within the body of the object. Ex: ferris wheel.

What is the relationship between tangential and rotational speed?

*v = rω* V = velocity (m/s) r = radius (meters) ω = radians/sec This says the linear speed is scaled by the radius just like how arc length varies by the radius. You move faster if the rate of rotation increases (bigger ω) or when you go farther from the axis (bigger r).

What are the three categories of satellites?

1) Low-earth orbit 2) Geo-stationary ring - stays at the same position on Earth 3) Non of the above

What is the equation to find centripetal accelerating?

An object in circular motion accelerates towards the center. Ac = v^2/r

What does it mean when it is said that centripetal acceleration is pointed to the center?

Each time - we want to go tangent to the line because of our inertia.

What is the universal gravitation equation?

Every object attracts each other with a force. The force is directly proportional the mass of each object. The greater the masses, the greater the force of attraction between them. IT els decreases as the square of the distance between the centers of the objet. It's the pull between the *centers* of the objects. Remember! It's force between them. The earth pulls the same amount on me as I pull on the Earth because it's an action reaction pair. This equation is derived because the force of gravity between two masses is proportional to the amount of mass and inversely proportional to the square of the separation distance Also, the distance is to the center of the object, not the surface

What are some examples of centripetal force?

For gravity, it's the earth's rotation. For normal, it's a graviton where you are smoothed against the wall keeping you in circular motion. For tension, it is spinning a ball around a string. For lift, it is a helicopter. For electricity, it is the atom. For friction, it's the friction force between a car's tires and the road causing the car to turn.

Which type of speed, angular or linear, is constant no matter the position or why?

If there is a meter stick going in a circle with two dots on it, one at the edge and one towards the middle, which is going faster? Rotational wise, they are the same because they make the same amount of rotations per second. But linear wise, the one on the outside goes a longer distance over the same time making it "faster."

What is rotational or angular speed?

Instead of saying 5 m/s we can say the number of rotations per unit of time. Some units for rotational speed include: - rpm (revolutions per minute) - radians/sec (SI unit, denoted by ω) 1 radian = 57.3 degree

How is the force of gravity affected by distance?

It follows the inverse square law. It reduces by a square amount. For example, the moon is 60x further from the center of the Earth than we are. Does that mean the gravitational force is 1/60? No! It's 1/60^2. Fg ~ 1/r^2

What is universal gravitation?

Newton generalized the moon finding to all objects and stated that all objects in the universe attract one another. Newton did not discover gravity. Newton discovered that gravity is universal. *Everything pulls on everything else in the universe in a way that involves only mass and distance*. Gravity acts center to center, as an inverse square law, and can be a centripetal force.

What was Newton's stroke of genius?

Newton reasoned that the moon is falling toward Earth for the same reason an apple falls from a tree - they are both pulled by Earth' gravity - gravity is universal.

Is there a net force on objects moving in circular motion?

Newton's first law states that "objects move in straight lines unless compelled to do otherwise." Since an object moving in a circle is curving, it must be acted on by a force. Therefore *there must be a net force acting on the object.*

What is revolution?

When an object turns around an *external* axis. Ex: the riders revolve around the Ferris wheel's axis.

What is so unique about circular motion?

One can engage it in but not go anywhere. This challenges our ideas of motion that have been linear up until now.

What is a non-inertial frame of reference?

One where Newton's law of inertia is not true. If we hold the puck on a string in a rotating room, it stands still. That makes one believe that there is force equal and opposite to balance out the tension - centrifugal force. But that's a fictions force - we don't know it because we are in a different perspective.

What is an inertial frame of reference?

One where Newton's law of inertia is true. For example, if a room is rotating and we look from above the room in a fixed position, and there is a guy with a string attached to a puck - we see the puck is moving in a circle because of the centripetal force applied by tension. Therefore, inertia is true.

What are frames of reference?

Our view of nature depends on the frame of reference from which we see it. Ex: In a fast moving vehicle, we have no speed at all relative to the vehicle but a lot of speed relative to the reference frame of the stationary ground outside. *So from one frame of reference we have speed, from another we none.* With a ladybug in a can in circular motion - from a stationary frame of reference we see there is no centrifugal force acting on the ladybug. However, we do see centripetal force. But *in the reference frame of the rotating system* the centrifugal force appears very real.

What are the two types of circular motion?

Rotation and revolution.

What is centrifugal force?

The apparent outward force on a rotating or revealing body. Centrifugal means "center-fleeing." Ex: When you are in a car that rounds a sharp turn, you pitch outward against the right door. Why? Not because of an outward centrifugal force but rather that there is no centripetal force holding you in circular motion. The "centrifugal-force effect" is attributed not to any real force but to inertia - the tendency of the moving body to follow a straight line-path. Therefore, while the force isn't real, the effect is real because we want to go in a straight line. Centrifugal force is an effect of rotation. It is not of an interaction and therefore it cannot be a true force. Therefore - it's a fictions force. But in a non-inertial frame such as the rotating system - it is very real.

What is the equation to find centripetal force?

The centripetal force on an object depends on the object's tangential speed, its mass, and the radius of its circular path. Centripetal force = mass*speed^2/radius of curvature Fc = mv^2/r Fc in newtons, m in kilograms, v in meters/sec, r in meters.

What is linear or tangential speed?

The distance traveled per unit of time. The linear speed is greater on the outer edge of a rotating object than is closer to the axis. Can also be called tangential speed because the *direction of motion is always tangent to the circle*. Tangential speed depends on rotational speed and the distance from the axis of rotation.

How did Newton reasoned that the moon orbit the Earth?

The moon is falling around the Earth. It falls beneath the straight line it would follow if no force acted on it. The moon is actually falling toward Earth but has great enough tangential velocity to avoid hitting Earth.

What is an axis?

The straight line around which rotation takes place.

What is the universal gravitational constant?

Universal gravitational constant, or g, describes the strength of gravity. G is the magnitude of force between two masses of 1 kilogram each, 1 meter apart: 6.67 x 10^-11 Nm^2/kg^2

If there is net force on circular motion, does it accelerate?

When there are net forces, acceleration must be created. But how you may ask - it's not changing speed! But acceleration is not just change in speed but also a change in direction. Therefore, circular motion is a type of accelerated motion even when speed is constant.

In a car that's making a turn, why do we go towards the other side of the car?

While it feels like a force is pulling us there - it is because we are in a non-inertial frame - centrifugal is fictions. It is because of our straight line tendency to go to the other side.

What is the equation for the acceleration due to gravity?

g = Gm/r^2 Derived from w = mg. We can set mg = to the universal gravity constant equation because the force is the same!

The centripetal force acts at ____________ to the path of the moving object.

right angles, perpendicular