A particle P moves with constant angular speed around a circle whose center is at the origin and whose radius is R. The particle is said to be in uniform circular motion. Assume that the motion is counterclockwise and that the particle is at the point sR, 0d when t 0. The position vector at time t > 0 is rstd R cos t i 1 R sin t j. (a) Find the velocity vector v and show that v ? r 0. Conclude that v is tangent to the circle and points in the direction of the motion. (b) Show that the speed | v | of the particle is the constant R. The period T of the particle is the time required for one complete revolution. Conclude that T 2R | v | 2 (c) Find the acceleration vector a. Show that it is proportional to r and that it points toward the origin. An acceleration with this property is called a centripetal acceleration. Show that the magnitude of the acceleration vector is | a | R2 . (d) Suppose that the particle has mass m. Show that the magnitude of the force F that is required to produce this motion, called a centripetal force, is | F | m| v | 2 R

1/25/2017 Homework #1 • It must be completed on-line in McGraw Hill Connect. • Accessible after 5:00 p.m., January 26. • Closes at noon, February 7. • No deadline extension is allowed. • No discussion on the homework questions is allowed. • Chapters 1 through 3 covered. • Ten multiple-choice questions,10 points each. • You are allowed to re-do and re-submit it until the closing date. • Every time you submit it, you can find out what your total score is. • On-line signing up for Connect will close on January 31. GEOL 1303-003, Spring 2017 1 Igneous Rocks, Intrusive Activity, and the Origin of Igneous Rocks Physical Geology 15/e,