Question

Activity 8.5. Solve the following comprehensively. Box your final answers.

1. A 1.20kg disk with a radius of 10.0 cm rolls without slipping. The linear speed of the disk is 1.41m/s.

a. Find the translational KE.

b. Find the rotational KE.

c. Find the total kinetic energy.

Answer 1

(a)

$$KE_{t}=\dfrac{1}{2}mv^2,$$ $$KE_{t}=\dfrac{1}{2}\times1.2\ kg\times(1.41\ \dfrac{m}{s})^2=1.19\ J.$$

(b)

$$KE_r=\dfrac{1}{2}I\omega^2=\dfrac{1}{2}\times\dfrac{1}{2}mr^2(\dfrac{v}{r})^2=\dfrac{1}{4}mv^2,$$ $$KE_r=\dfrac{1}{4}\times1.2\ kg\times(1.41\ \dfrac{m}{s})^2=0.59\ J.$$

(c)

$$KE_{tot}=KE_t+KE_r=1.19\ J+0.59\ J=1.78\ J.$$