1. There is an analogy between rotational and translational physical quantities. Identify the rotational term analogous to each of the following linear quantities: acceleration, force, mass, work, translational kinetic energy, linear momentum, impulse. (Example: impulse F Delta-t corresponds to angular impulse, tau Delta-t . (Greek letters don't always work correctly in HTML on different browsers, so I will just spell them out.)
2. An automobile with tires of radius 0.260 m travels 80,000 km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in the radius due to wear?
3. Vinyl record albums revolve 33.33 times per minute. What is this in revolutions per second? In radians per second?
4. Suppose a phonograph record accelerates from rest to 33.3 rpm in 1.50 s. (a) What is its angular acceleration in rad/s^2? (b) How many revolutions does it go through in the process?
5. Helicopter blades withstand tremendous stresses. In addition to supporting the weight of the helicopter, they are spun at rapid rates and experience large centripetal accelerations, especially at the tip. (a) Calculate the centripetal acceleration at the tip of a 4.00 m long helicopter blade that rotates at 300 rpm. (b) Compare the linear speed of the tip with the speed of sound (taken to be 340 m/s this day.)
The solution provides a detailed and step-by-step explanation for the problem.