Question

A wheel 1.0m in diameter rotates with an angular acceleration of 40rad/sec^2.
A, if the wheels initial velocity is 2.0rad/sec, what is its angular velocity after 10sec?
B, through what angle does it rotate in the 10sec interval?
C, what are the tangential speed and acceleration of a point on the rim of the wheel at the end of the 10 sec interval?

Answer 1

a)

$$\omega=\omega_0+\alpha t=2+40(10)=402\frac{rad}{s}$$

b)

$$\theta=\omega_0t+0.5\alpha t^2=2(10)+0.5(40)(10)^2\\=2020\ rad$$

c)

$$v=\omega r=402(1)=402\frac{m}{s}$$

$$a_t=\alpha r=40(1)=40\frac{m}{s^2}$$