Determine the following rotational quantities. Make assumptions or estimates where appropriate.

A) What is the magnitude of the angular velocity of the Earth in its orbit around the Sun?

B) What is the magnitude of the angular velocity of a wheel in a car driving on the interstate. (state all assumptions)

C) What is the magnitude of the angular acceleration of a gyroscope that starts out spinning at 53 Hz and takes 7.2 s to slow down to zero?

D) A spinning neutron star, with a period of 4.3 ms, is slowing with an angular acceleration of 2.4x10-8 s-2. How many years will it take for it to stop spinning?

4. A car of mass m is traveling with constant speed v around a circular banked road of radius R, see the

side view and the free-body diagram.
a) Apply Newton’s 2nd law to the car, i.e. write equations for the centripetal, angular, and vertical components of the net force.
b) Determine the angle θ at which the road should be banked so that no static friction is required to drive the car.
Now, include the static friction force FS in the free-body diagram and Newton’s equations.
c) Find the maximum speed vmax at which the car can travel around without slipping. Assume the coefficient of maximum static friction is μs.
In the end, find the expressions for the contact force with which the ground is acting on the car, i.e.:
d) The magnitude of the normal force FN and
e) The magnitude of the static friction FS, in terms of the given quantities m, v, R, g, and θ.

A physics instructor wants to project a spectrum of visible-light colors from 400 nm to 700 nm as part of a classroom demonstration. She shines a beam of white light through a diffraction grating that has 600 lines per mm, projecting a pattern on a screen 2.9 m behind the grating.

How wide is the spectrum that corresponds to m = 1? Express your answer with the appropriate units.

How much distance separates the end of the m = 1 spectrum and the start of the m = 2 spectrum?

a 1.0 x 10³ kg toyota collides into the rear end of a 2.2 x 10³ kg cadillac stopped as a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer,knowing that the coefficient of kinetic friction between the tires and the road was .4 calculated the speed of the toyota at impact. What was that speed? Please show the steps that got you to the answer as that is what I am interested in! thanks

As simply as you can but with complete and comprehensive detail, state and explain each of Newtons Three Fundamental Laws of Motion. After you have explained all Three Laws look come up with and explain an example problem of your own. It must include an explanation of how at least one of Newton's laws is used if not more than one. (can not use online sites)

Now let's consider the impulse associated with kicking a soccer ball (Figure 1). The ball has mass 0.40 kg . Initially it moves horizontally to the left at 20 m/s, but then it is kicked and given a velocity with magnitude 30 m/s and direction φ=45∘ upward and to the right. Find the impulse of the force and the average force on the ball, assuming a collision time Δt=0.010s.

angle: 27

Part A:Suppose the ball is moving at 30 ∘ downward from the horizontal before it is kicked. If all the numerical values are the same as before, find the magnitude of the average force on the ball. Express your answer in newtons to two significant figures.

Part B:Find the direction of the average force on the ball found in Part A. Express your answer in degrees to two significant figures.

Suppose that an event occurs in the reference frame S with coordinates x = 2m, y = 0m and z = 0m at t = 4m/c. The frame S’ moves in the positive x-direction with velocity u = 0.2c. The origins of S and S’ coincide at t = t’ = 0. a. Use the Lorentz transformations to find the coordinates of the event in S’. b. Use the inverse transformation on the results of (a) to obtain the original coordinates and time.

The trajectory of a rock thrown from a height with an initial speed of 19.7 m/s is shown in the figure below. Evaluate the magnitude of the gravitational field at the surface of the planet. The planet has no atmosphere.

How do you determine what velocity and angle is needed so that both the x and y displacement are equal to each other at a specific point?

For example if a projectile is launched on a 100m cliff, what velocity and angle is needed so that both the x and y displacement points are equal to 160m?

Which of the following inertial reference frames are proper frames for the two events listed? Choose all that apply.

RED FRAME: Event A happened at a different place than event B.

ORANGE FRAME: Event C happened at (-7 m, 3 m, 4 m) and event D happened at (-7 m, 3 m, 5 m).

YELLOW FRAME: The distance between where event E occurred and where event F occurred was 0 m.

GREEN FRAME: A rocket was traveling at a constant velocity when it passed through a stationary tunnel. Event G was the front of the rocket entering the tunnel and event H was the the front of the rocket leaving the tunnel.

BLUE FRAME: A stationary rocket was engulfed by a hollow cylinder that was moving at a constant velocity. Event J was the front of the rocket entering the cylinder and event K was the the front of the rocket leaving the cylinder.

A pitcher rotates his arm to throw a baseball. The distance from the centre of rotation of the pitcher's arm to his hand is 110 cm and remains constant over the throw. At the start of the throw, the pitcher's arm is already rotating at 0.250 rad/s and it takes him 250 ms to complete the throw. if the arc length that his hand traces over the throw is 2.70m, calculate the transverse velocity of his hand at the end of the throw.

Which one would have the biggest impact? Why?

A 200-g ball is dropped from rest from a height of 1.4 m. It bounces and returns to the same position.  

a) What is the change in momentum between the two points?

b) If the ball is in contact with the floor for 10-³ s, what impulse does the floor impart to the ball?  

In these cases remember vectors.

Write out the matrix based on the secular equations for benzene using the huckel approximation.

1. At what speed does a 1700 kg compact car have the same kinetic energy as a 1.80×10⁴ kg truck going 23.0 km/hr ?

2.The cable of a crane is lifting a 850 kg girder. The girder increases its speed from 0.25 m/s to 1.25 m/s in a distance of 3.5 m.

Part 1: How much work is done by gravity? Express your answer with the appropriate units.

Part 2: How much work is done by tension? Express your answer with the appropriate units.