Answer to Question #246136 in Molecular Physics | Thermodynamics for Kelani

Question

A bicyclist starting at rest produces a constant angular acceleration of 1.50 rad/s² for wheels that are 33.5 cm in radius.

(a) What is the bicycle's linear acceleration (in m/s²)? (Enter the magnitude.)

___ m/s²

(b) What is the angular speed of the wheels (in rad/s) when the bicyclist reaches 10.2 m/s?

___rad/s

(c) How many radians have the wheels turned through in that time?

___rad

(d) How far (in m) has the bicycle traveled?

___m

Answer 1

$α=1.50 \;rad/s^2 \\ r = 33.5 \;cm$

(a)

$a = rα \\ = 33.5 \times 10^{-2} \times 1.50 \\ = 0.5025 \;m/s^2$

(b)

$v=rω \\ ω = \frac{v}{r} \\ = \frac{10.2}{0.335} \\ = 30.44 \;rad/s$

(c)

$v=u+at \\ u=0 \;(at \;rest) \\ 10.2 = 0 + 0.5025t \\ t = 20.30 \;sec \\ ΔQ=\frac{1}{2} αt^2 \\ = \frac{1}{2} \times 1.5 \times (20.30)^2 \\ = 309.06 \;rad$

(d) Distance

$s=rΔQ \\ = 0.335 \times 309.06 \\ = 103.53 \;m$