Question

1. A circular disk of radius 30 cm is rotating with an angular velocity of 2 radians / s. What is the tangential velocity of a point on the rim of the disk? What is its centripetal acceleration?

Answer 1

Speed v: distance/time

Angular speed w: angle/time

If a body moves along a circle circumference,

then 360 degrees of motion (2pi [rads]) are equivalent to

2pi radiuses of distance, which helps us say: $v = wr$

Angular velocity: x rads/s == x radiuses in one second

Angular acceleration: $(x \cdot \text{rad/s}) / (s == x \cdot (1 \cdot \text{rad/s}))$ speeds in one sec.

The tangential acceleration is the acceleration that shows how much the measure of speed (= velocity) gets different along the path of motion [>>> equivalent of angular acceleration in terms of distance], while the centripetal acceleration shows how much the direction of speed (= velocity) changes.

Similarly, then,

tangential acc. = angular acc. x radius, while

centripetal force: $|F| = m|a| = \frac{m}{2} r$.