2 forces are acting on an object, the object is in equilibrium if...
the net force and the net torque on then object are equal to 0
A sold disk and a hoop are both released simultaneously from the top f an incline without slipping. Which reaches the bottom first?
A mouse is initially at rest on a horizontal turntable mounted on a frictionless, vertical axle. As the mouse begins to walk clockwise around the perimeter, what must be true of the turntable?
It turns counterclockwise because angular momentum is conserved.
Bernoulli's equation can be used to explain, in part, what phenomena?
-lift of an airplane wing in flight
-curve of a spinning baseball
-reduction of pressure of moving fluids
A boat develops a leak and, after its passengers are rescued, eventually sinks to the bottom of a lake. When the boat is at the bottom, which of the following statements is true?
-The normal force of the boat is less than the weight of the boat
Three vessels of different shapes are filled to the same level with water as in the figure below. The area of the base is the same for all three vessels. What is true about the pressure?
-the pressure at the bottom of each vessel will be equal
A hose is pointed straight up, with water flowing from it at a steady volume flow rate and reaching a maximum height of h. Neglecting air resistance,what adjustments to the nozzle will result in the water reaching a height of 4h?
-decrease the area by a factor of 2.
A simple pendulum consists of a small object of mass 3.6 kg hanging at the end of a 2.0 m long light string that is connected to a pivot point. Does the torque increase or decrease as the angle increases?
-Torque will increase with the angle increase
The gravitational force exerted on an astronaut on Earth's surface is 650 N down. When she is in the International Space Station, what statement is true?
-the gravitational force on the astronaut will be smaller than 650N, but not zero
Consider an object on a rotating disk a distance r from its center, held in place on the disk by static friction. What statements would be true concerning this object?
-The object has a tangential acceleration only if the disk has an angular acceleration.
-If the angular speed is constant, the object must have constant tangential speed.
-If the disk has an angular acceleration, the object has both a centripetal and a tangential acceleration.
-The object always has a centripetal acceleration except when the angular speed is zero.
A merry-go-round rotates with constant angular speed. As a rider moves from the rim of the merry-go-round toward the center, what happens to the magnitude of total centripetal force that must be exerted on him?
A satellite moves in a circular orbit at a constant speed around Earth. What statement is true?
The satellite has an acceleration directed toward Earth.
A wooden block floats in water, and a solid steel object is attached to the bottom of the block by a string as in the figure below. If the block remains floating, which of the following statements is valid?
-The tension in the string is less than the weight of the steel object.
-The buoyant force on the block is equal to the weight of the volume of water it displaces.
A solid iron sphere and a solid lead sphere of the same size are each suspended by strings and are submerged in a tank of water. (Note that the density of lead is greater than that of iron.) Which of the following statements are valid? (Choose all correct statements.)
-The buoyant force on each is the same.
-The tension in the string supporting the lead sphere is greater than the tension in the string supporting the iron sphere.
Uniform Circular Motion
-when object moves in circular motion at a constant speed
-Since direction is changing there is acceleration
- fictitious force
Merry Go Round Example
-The faster you go, it feels like there is an increasing force pushing you away from the center of the merry-go-round.
-This is not true. There is actually the lack of a force keeping you moving in a circle.
Merry Go Round Example Continued
-According to Newton's 1st Law, your body wants to continue to move in a straight line of constant velocity and if you don't hold on or hold yourself against a bar (adding centripetal force), you will move in a straight line off the merry-go-round.
Angular Speed/Acceleration of a rigid object on a fixed axis
-every portion of the object has the same angular speed and angular acceleration.
-ie: merry go round or bike wheel
-direction of velocity vector is tangent to the circular path
-magnitude of v is linear speed v=vt
Tangential Speed of a point on a rotating object...
-equals the distance of that point from the axis of rotation multiplied by the angular speed
-every point on the rotating object has the same ANGULAR SPEED
-Even though a car is moving at a constant speed, it still has acceleration because velocity (magnitude with direction) is changing.
-the acceleration vector is pointing toward the center which is centripetal acceleration
Newtonian Gravitation (Gauss's Law)
-Gravitational force exerted by a uniform sphere on a particle outside the sphere is the same as the force exerted if the entire mass of the sphere were concentrated at its center
Center of Gravity
-of a solid object is the point where its entire weight can be considered to act when calculating the torque due to the weight of the object.
Torque (Seesaw Example)
-Balanced torques happen on a seesaw when two children of different weights sit at different positions
-heavier kid sits toward the center, lighter toward the edge; creates equilibrium/ center of gravity
Center of Gravity
-point around which a body's mass is equally distributed in all directions
-uniform object is the mid point
Center of gravity (outside an object)
-example is a hoop where the center of gravity would be in the middle instead of actually on the object
Moment of Inertia
-tells us how difficult it is to rotate the object
-depends on how the mass is distributed nd the location of the axis of rotation
-a rotating object tends to stay at the same angular speed unless an outside force acts upon it. (newton's 1st law)
-Sphere would win because mass is evenly distributed evenly making inertia greater
Conservation of Angular Momentum
-if no unbalanced torque acts on a rotating system, the angular momentum of that system is constant
-Reducing r makes v greater to have same angular momentum