physics questions

  
1. in class we did a demonstration of a spinning tire being held up by a rope attached to an axel that extended about 20 cm out from the center of the tire. if we didnt spin the tire and tried to hold it up by a rope attached to the end of the axel, it fell over as we would expect. if we spun the tire and then tried to hold it up by the rope it didnt fall over. using a force diagram and words like torgue and angular momentum. explain why the tire doesnt fall over.
2. The Earth is both rotating around the Sun and rotating around its axis of rotation (which is a line from the south pole to the north pole), thus is has two types of angular momentum, which are called spin angular momentum and orbital angular momentum. Both types of angular momentum point in the same direction. The Earth has a mass of 5.972 x 1024 kg, a mean radius of 6370 km, and an average distance from the Sun of 1.5 × 1011 m. Does the Earth have more spin angular momentum or orbital angular momentum?
3. A Ballistic pendulum is a device used for measuring the velocity of bullets or other objects moving too fast to reliably measure with a photograph. A ballistic pendulum works by firing a bullet into a block. The bullet gets lodged in the block and then the bullet and the block swing up to some angle θ, which can be easily measured. Derive a formula for the initial velocity of the bullet V0 in terms of the mass of the bullet m, the mass of the block M, the length of the pendulum L, and the maximum angle of the pendulum θ. Hint: assume that the moment of inertia is just (m+M)L2.

4. A mass of 3.4 kg is attached to a spring with a spring constant of 0.29N/m. find the period of oscillation for this system
5.  A mass of 3.4 kg is attached to two identical springs with spring constants of 0.29 N/m, with one spring on each side. Write Newton’s 2nd law for this system, show that x(t) = x0 sinωt is a solution, and find the value of ω.
6. For medical reasons astronauts need to monitor their weight very closely when they spend significant amounts of time on the international space station, however since they are in free-fall a normal bathroom scale won’t work. Instead astronauts use a scale that consists of a harness they strap themselves into attached to a spring that’s attached to a wall. They then pull themselves away from the wall, stretching the spring, and release themselves. They measure the period of their oscillation on the spring. If the spring has a spring constant of 3000 N/m and you measure an angular frequency of 5.9 rad/s, what is the astronaut’s mass?
7. You have a grandfather clock with a pendulum that is used to keep time. The period of oscillation of the pendulum should be 1 s, but you find that your clock is running slow by 1 minute every day. Find the ratio of the correct length of the pendulum to the current incorrect length.
8. You live in Chico (elevation 197 ft) and own a grandfather clock that keeps perfect time, meaning that the period of oscillation of its pendulum is exactly 1 s. In Chico acceleration due to gravity is gc 9.798 m/s2. You move to Leadville, Colorado (elevation 10,152 ft) where acceleration due to gravity is gL = 9.783 m/s2. What is the new period of the pendulum in your grandfather clock?