Answer to Question #90434 in Mechanics | Relativity for AWESOME

Question

An object makes 240rpm on a circle of radius 2m. calculate i. its period ii. Angular velocity iii. Linear velocity iv. Centripetal acceleration v. angular acceleration.

Answer 1

i. Period. 

Object makes 240/60 = 4 resolution per second (rps). So its period is equal

$$T = 1/4 =0.25\ s.$$

ii. Angular velocity. 

Angular velocity ω is the rate of change of an angle. For one resolution the angle is changed to 2π radians, so for 4 rps the changing of angle is equal 

$$\omega = 2\pi*4 = 8\pi = 25.12\ rad/s.$$

iii. Linear velocity 

During one period T, a point located on the edge of the object will passed the distance wich is equal the object circumference. From simple equation 2πr = vT the linear velocity is 

$$v = \frac{2\pi r}{T}=\frac{2*2*\pi}{0.25} = 16\pi = 50.24\ m/s.$$

iv. Centripetal acceleration can be found using the formula

$$a_c = \frac{v^2}{r} = \frac{(16\pi)^2}{2} = 128\pi^2 = 1262 \ m/s^2.$$

v. Angular acceleration.

Angular acceleration is the rate of change angular velocity which is constant, so the answer is 0.