Rotation Angular Velocity and Angular Acceleration PHYS116 A01

Rotation, Angular Velocity and Angular Acceleration PHYS-116 A-01, 1/3/10, Lecture 21 Momchil Velkovsky

Angular motions in revolutions, degrees, and radians • One complete cycle of 360° is one revolution. • One complete revolution is 2π radians. • Relating the two, 360° = 2 π radians or 1 radian = 57. 3°.

Angular velocity ¡ The angular velocity is the angle swept out divided by the time it took to sweep out the angular displacement. ¡ Angular velocity is denoted by the symbol ω (omega). ¡ Angular velocity is measured in radians per second (SI standard) as well as other measures such as r. p. m. (revolutions per minute).

Compared to a gear tooth on the rear sprocket (on the left, of small radius) of a bicycle, a gear tooth on the front sprocket (on the right, of large radius) has ¡ ¡ ¡ A. a faster linear speed and a faster angular speed. B. the same linear speed and a faster angular speed. C. a slower linear speed and the same angular speed. D. the same linear speed and a slower angular speed. E. none of the above

The graph shows the angular velocity and angular acceleration versus time for a rotating body. At which of the following times is the rotation speeding up at the greatest rate? ¡ ¡ ¡ A. t = 1 s B. t = 2 s C. t = 3 s D. t = 4 s E. t = 5 s

Angular velocity is a vector • You can visualize the position of the vector by sweeping out the angle with the fingers of your right hand. The position of your thumb will be the position of the angular velocity vector. This is called the “right-hand rule. ”

A DVD is rotating with an ever-increasing speed. How do the centripetal acceleration arad and tangential acceleration atan compare at points P and Q? ¡ ¡ A. P and Q have the same arad and atan. B. Q has a greater arad and a greater atan than P. C. Q has a smaller arad and a greater atan than P. D. P and Q have the same arad, but Q has a greater atan than P.

We have three fundamental equations for the kinematics of constant angular acceleration

Rotational energy ¡ Just like linear kinetic energy is ½ mv 2, the angular energy will be determined by ½ Iω2.

Finding the moment of inertia for common shapes