For the definitions please include the equations to:

A:Give a definition of the torque as a vector. Briefly describe torque.

B: Give a definition of the angular acceleration. Briefly describe angular acceleration.

C: Give a definition of the moment of inertia.

City A is located 40° N, 10° W. City B is located 40° N, 20° E. Assume the Earth is a perfect sphere with a radius of 6371km.

Calculate the short distance between city A and city B along the 40° N parallel.

Calculate the shortest distance (on curved Earth surface) between city A and the equator. π = 3.141

The coefficients of static and kinetic friction between a 50 kilogram box and a horizontal surface are 0.60 and 0.40, respectively. (a) What is the acceleration of the object if a 250 newton horizontal force is applied to the box? (b) What if the applied force is 350 N?

Assume a satellite communication system based upon a highly elliptical polar orbit approximately centered over the Atlantic Ocean. Communication is to be maintained between a U.S. station and one in the United Kingdom. The frequency of operation is a 435-MHz uplink and 145-MHz downlink.

Discuss the type of antennas that might be used for both uplink and downlink. What are the implications—pros and cons—of each type? Will tracking or positioning equipment be needed? If so, for which types of antennas? Will communication ever be interrupted; if so, when?

A ball is released from the top of the building and reaches the ground after 5 seconds (15 points). a) What is the velocity of the ball when it hits the ground? b) What is the height of the building? c) How much the ball falls in the last 2 seconds of the motion?

At a distance of 60.0km from a radio station antenna the electric-field amplitude is 8.70�10^?2V/m

Part B

Assuming that the antenna radiates equally in all directions (which is probably not the case), what is the total power output of the station? in W

Part C

At what distance from the antenna is the electric-field amplitude equal to half the value given? in km

At the equator, the earth’s field is essentially horizontal; near the north pole, it is nearly vertical. In between, the angle varies. As you move farther north, the dip angle, the angle of the earth’s field below horizontal, steadily increases. Green turtles seem to use this dip angle to determine their latitude. Suppose you are a researcher wanting to test this idea. You have gathered green turtle hatchlings from a beach where the magnetic field strength is 50 μT and the dip angle is 56∘. You then put the turtles in a 2.0 m diameter circular tank and monitor the direction in which they swim as you vary the magnetic field in the tank. You change the field by passing a current through a 100-turn horizontal coil wrapped around the tank. This creates a field that adds to that of the earth.

A.) In what direction should current pass through the coil, to produce a net field in the center of the tank that has a dip angle of 62∘ ? [ANSWER: CLOCKWISE]
B.) What current should you pass through the coil, to produce a net field in the center of the tank that has a dip angle of 62∘ ?

Please show step-by-step solution. Thank you!

A potter is making a spherical vase on a potter’s wheel. The vase has a mass of 0.8 kg and a radius of 4.0 cm and the potter’s wheel has a mass of 20.0 kg and a radius of 20.0 cm. The vase is centered on the wheel. While working on the vase, the wheel and vase rotate at 1 revolution every four seconds. When finished with the vase, the potter slows the wheel (and vase) by applying a normal force at the edge of the wheel. If she brings the wheel to a complete stop in 30 s and the coefficient of friction between her hands and the wheel is 0.45, what is the magnitude of the normal force between each hand and the wheel.

6. Use the periodic chart to fill in all the missing items so as to make the nuclear decays complete. I.e., specify completely (i.e. including subscripts and superscripts) Z and X in each of the two separate reactions below.

92^238U + 0^1 n --> 57^140La + Z + 2 0^1n

88^226Ra --> X + 2^4 He

A computer-controlled racecar is programmed to execute the following motion along the ground for 6.0 seconds. Let’s say the car begins at the origin of our coordinate system. Its initial velocity is ~v0 = (15:0 m/s)^i and its acceleration is constant: ~a = (?6:0 m/s2)^i + (?2:0 m/s2)^j

(a) Make a table, and calculate the car’s position vector, ~r at the end of each second, through t = 6:0 seconds. Use these data to plot the trajectory of the particle for this time interval. You can do it by hand on the axes given to you on the last page. (If you like, you could also do this by writing a computer program that would calculate hundreds of data points).

(b) On your graph, sketch vectors for both the car’s velocity and acceleration at t = 1:0; 2:0 and 4.0 seconds. At each of these instants, is the car speeding up or slowing down? How do you know?

(c) You may have found that judging the answer to part (b) was a tough call for t = 2:0 s. We can do this conclusively: i. Find both the velocity and the speed of the particle at t = 2:0 seconds. ii. At t = 2:0 seconds, find the rate at which the car’s speed is changing (Note that I’m not asking the rate at which its velocity is changing, which is just j~aj). (Hint: you’ll need to find the angle between ~v and ~a, which is something for which the vector dot product is very useful... ) iii. At what time is the rate of change of the car’s speed equal to zero, and what is the car’s speed at this instant? 3

(a)A cosmic ray proton streaks through the lab with velocity 0.82c at an angle of 52° with the +x direction (in the xy plane of the lab). Compute the magnitude and direction of the proton's velocity when viewed from frame S' moving with β = 0.74.

(b) Suzanne observes two light pulses to be emitted from the same location, but separated in time by 3.50 µs. Mark sees the emission of the same two pulses separated in time by 8.00µs.

How fast is Mark moving relative to Suzanne?c

According to Mark, what is the separation in space of the two pulses?

m

Two stars of equal mass orbit one another. (This is called a binary star system.) If the stars’ orbits have a semimajor axis of 2.5x10^8 km and complete one orbit every 2.4 years, what is the mass of each star? pick from: (8.1x10^29 kg, 1.6x10^30 kg, 8.1x10^20 kg, 1.6x10^21 kg)

A satellite orbits a planet at a distance r. If it has a circular orbit, the total energy (E=K+U) of the satellite is equal to:

Hint: F_centripetal=mv^2/r pick from: (E=0, E=-U/2, E=U, E=U/2)

A probe is brought to rest a distance of 1.5x10^11 m from the Sun, and allowed to fall directly into the Sun. How fast will the probe be moving when it collides with the Sun? The mass of the Sun is 2.0x10^30 kg, and its radius is 7.0x10^8 m. Hint: Consider energy conservation. pick from: (620 km/s, 42 km/s, 1.8x10^6 km/s, 3.8x10^5 km/s)

A neutron in a nuclear reactor makes an elastic, head-on collision with the nucleus of a carbon atom initially at rest.

(a) What fraction of the neutron's kinetic energy is transferred to the carbon nucleus? (The mass of the carbon nucleus is about 12.0 times the mass of the neutron.)

__________

b) The initial kinetic energy of the neutron is 2.70 10-13 J. Find its final kinetic energy and the kinetic energy of the carbon nucleus after the collision.

neutron __________J

carbon nucleus __________J

Inez is putting up decorations for her sister's quinceanera (fifteenth birthday party). She ties three light silk ribbons together to the top of a gateway and hangs from each ribbon a rubber balloon. To include the effects of the gravitational and buoyant forces on it, each balloon can be modeled as a particle of mass m=2.79 g, with its center 48.7 cm from the point of support. To show off the colors of the balloons, Inez rubs the whole surface of each balloon with her woolen scarf, to make them hang separately with gaps between them. The centers of the hanging balloons form a horizontal equilateral triangle with sides 30.2 cm long. What is the common charge each balloon carries?