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A disk of radius 14 cm, initially at rest, begins rotating about its axis with a constant angular...

Question:

A disk of radius 14 cm, initially at rest, begins rotating about its axis with a constant angular acceleration of 7.1 rad/s{eq}^2 {/eq}. What are the following values at t = 7.0 s?

(a) the angular velocity of the disk

(b) the tangential acceleration at and the centripetal acceleration ac of a point at the edge of the disk

Rotational Motion

Rotational motion is the motion of objects revolving or rotating around an axis. Most of the kinematic equations that govern rotation motion are analogous to those that govern linear motion.

Answer and Explanation:

Given

{eq}\bullet \text{Radius of disk}\ r = 0.14 m\\ \bullet \text{Angular Acceleration}\ \alpha = 7.1 rad/s^2\\ \bullet \text{Time}\ t = 7.0s\\ {/eq}

Part A

The angular velocity can be found as follows

{eq}\omega = \alpha t = 7.1rad/s^2*7.0s = 49.7rad/s {/eq}

Part B

The tangential acceleration can be found by converting to a linear acceleration

{eq}a_t = \alpha r = 7.1rad/s^2*0.14m = 0.99m/s^2 {/eq}

The centripetal acceleration can be found using the following formula

{eq}a_c = \omega^2 r = (49.7rad/s)^2*0.14m = 6.96 m/s^2 {/eq}


Learn more about this topic:

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Practice Applying Rotational Motion Formulas

from Physics 101: Help and Review

Chapter 17 / Lesson 15
870

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