Question

A wheel 1.0 m in radius rotates with an angular acceleration of 4.0rad/s2

1) If the wheel’s initial angular velocity is 2.0 rad/s, its angular velocity after 10 s is

2)The angle in radians it rotates in the 10-s interval is

3)The tangential speed of the point on the rim of the wheel at the end of the 10-s interval is

4)The tangential acceleration of the point on the rim of the wheel at the end of the 10-s interval is

Answer 1

1) If the wheel’s initial angular velocity is 2.0 rad/s, its angular velocity after 10 s is

$$\omega_f=\omega_i+\alpha t=2+4·10=42\text{ rad/s}.$$

2) The angle in radians it rotates in the 10-s interval is

$$\phi=\omega_it+\frac{\alpha t^2}{2}=220\text{ rad}.$$

3) The tangential speed of the point on the rim of the wheel at the end of the 10-s interval is

$$v=\omega_fR=42·1=42\text{ m/s}.$$

4) The tangential acceleration of the point on the rim of the wheel at the end of the 10-s interval is

$$a=\alpha R=4·1=4\text{ m/s}^2.$$