Question

Wheel with radius R = 10 cm, rotates with a constant angular acceleration = 3.14 rad / s². Find: a) angular velocity b) linear velocity c) tangential acceleration d) centripetal acceleration e) full acceleration f) the angle formed by the direction of acceleration of the point with the radius of the wheel. of the first second after the start of the movement.

Answer 1

(a) We can find the angular velocity as follows:

$$\omega=\omega_0+\alpha t,$$ $$\omega=0+3.14\ \dfrac{rad}{s^2}\cdot1\ s=3.14\ \dfrac{rad}{s}.$$

(b) We can find the linear velocity as follows:

$$v=\omega r=3.14\ \dfrac{rad}{s}\cdot0.1\ m=0.314\ \dfrac{m}{s}.$$

(c) We can find the tangential acceleration as follows:

$$a_t=\alpha R=3.14\ \dfrac{rad}{s^2}\cdot0.1\ m=0.314\ \dfrac{m}{s^2}.$$

(d) We can find the centripetal acceleration as follows:

$$a_c=\omega^2R=(3.14\ \dfrac{rad}{s})^2\cdot0.1\ m=0.986\ \dfrac{m}{s^2}.$$

(e) We can find the full acceleration from the Pythagorean theorem:

$$a=\sqrt{a_c^2+a_t^2}=\sqrt{(0.986\ \dfrac{m}{s^2})^2+(0.314\ \dfrac{m}{s^2})^2}=1.03\ \dfrac{m}{s^2}.$$

(f) We can find the angle as follows:

$$\theta=\dfrac{1}{2}\alpha t^2,$$ $$\theta=\dfrac{1}{2}\cdot3.14\ \dfrac{rad}{s^2}\cdot(1\ s)^2=1.57\ rad.$$