The angular velocity of a spinning gyroscope is measured every 0.5 s. The results and the best-fit line from a spreadsheet are shown in FIGURE P4.63. What is the gyroscope's initial angular velocity at t = 0 s?

While driving north at 25 m/s during a rainstorm you notice that the rain makes an angle of 38° with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these observations, determine the speed and angle of the raindrops relative to the ground.

A typical laboratory centrifuge rotates at 4000 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. What is the acceleration at the end of a test tube that is 10 cm from the axis of rotation?

A typical laboratory centrifuge rotates at 4000 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. For comparison, what is the magnitude of the acceleration a test tube would experience if dropped from a height of 1.0 m and stopped in a 1.0-ms-long encounter with a hard floor?

Ships A and B leave port together. For the next two hours, ship A travels at 20 mph in a direction 30° west of north while ship B travels 20° east of north at 25 mph. What is the speed of ship A as seen by ship B?

A cannonball is fired at 100 m/s from a barrel tilted upward at 25°. What is the angle after the cannonball travels 500 m?

A ball rolling on a circular track, starting from rest, has angular acceleration $\alpha$. Find an expression, in terms of $\alpha$, for the time at which the ball's acceleration vector a is ${45}^{\circ }$ away from a radial line toward the center of the circle.