Question

 A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T, as shown.

 Derive a formula for the bullet speed u in terms of D, T, and a measured angle e between the position of the hole in the first disk and that of the hole in the second. If required, use r, not its numeric equivalent. Both of the holes lie at the same radial distance from the shaft. θ measures the angular displacement between the two holes; for instance, θ = 0 means that the holes are in a line and θ = π means that when one hole is up, the other is down. Assume that the bullet must travel through the set of disks within a single revolution.

 A bicycle wheel is rotating at 46 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.42 rad/s².

 What is the wheel's angular velocity, in rpm, 8.0 s later?

 Part B

 How many revolutions does the wheel make during this time?

 A rock thrown with speed 12.0 m/s and launch angle 30.0° (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g =9.800 m/s2 for the free-fall acceleration..

 Part D

 A second rock is thrown straight upward with a speed 6.000 m/s. If this rock takes 1.828 s to fall to the ground, from what height H was it released?

Answer 1

1. let t be the time the bullet travels between the disks, and v the speed of the bullet

D = vt

with in this time the disk must have an angular displacement , which the angle between the holes, so that the bullet passes through the second hole

T is the period of rotation

t must be same from both the above expressions so that the bullet passes through the two holes

t = D/v = T/2

speed of the bullet v = 2D/T