Question

Physics Help!!! Your car tire has a diameter of 3m and is rotating at 4 rev/s, when suddenly Bob slams his foot down on the accelerator. After traveling 400 m, the tire's rotation has increased to 10 rev/s. What was the tire's angular acceleration?

Answer 1

to solve this you need equations for angular velocity and angular displacement
\[v(t) = at +v_0\]
\[r(t) = \frac{a}{2}t^{2} +v_0 t + r_0\]
initial values:
v_0 = 4 , r_0 = 0
final values:
v = 10 , r = 400/3pi
**Note, r(t) gives the amount of revolutions not distance in meters
plugging in these values
\[10 = at +4 \rightarrow at = 6 \rightarrow t = \frac{6}{a}\]
\[\frac{400}{3\pi} = \frac{a}{2}t^{2} +4t\]
substitute for t in 2nd equation to solve for a