Starting from rest, you ride your bike with a constant acceleration and reach a

Question

Starting from rest, you ride your bike with a constant acceleration and reach a speed of 15.0 miles/hr in a time of 20.0 s and thereafter you maintain that constant speed. The wheel has a radius R=0.300 m.

(a) Calculate the angular acceleration of the wheel.

(b) Calculate the final angular speed of the wheel (reached at the end of the acceleration period).

(c) How many revolutions does the wheel make in that time?

(d) When you are riding with a constant speed, does a piece of gum which got stuck to the rim of the wheel have a centripetal acceleration? Explain. If yes, calculate this acceleration.

(e) When you are riding with a constant speed, oes a piece of gum which got stuck to the rim of the wheel have an angular acceleration? Explain. If yes, calculate this acceleration.

(f) During the acceleration period, what kind of acceleration(s) does the piece of gum have? Explain.

Explanation / Answer

Given Data: Speed of the bike, v = (15 miles / hr )(1609.34 m / 1 mile)(1 hr/3600 s)                                  = 6.7 m/s The wheel has a radius R=0.300 m Time interval, t = 20.0 s Solution: a) Angular acceleration of the wheel is,                       = t                        = (v/ R) / t                            = (6.7 m/s / 0.3 m) / 20 s                            = 1.116 rad/s ------------------------------------------------------------ (b) Final angular speed of the wheel is,                     = v / R                          = 6.7 m/s / (0.3 m)                          = 22.3 rad/s ------------------------------------------------------------- c ) Number of revolutions made by the wheel is,                      = 1/2 t2                         = 1/2 (1.116 rad/s2) (20.0 s)2                         = 223.2 rad               1 rad = (1/2) rev        223.2 rad = 35.5 revolutions -------------------------------------------------------------------- d) Yes, the gum will possess centripetal acceleration,                  a = v2 / R                      = (6.7 m/s)2 / 0.3 m                      = 149.6 m/s2 ---------------------------------------------------------------------- e) The angular acceleration of the gum is,                       = 1.116 rad/s ------------------------------------------------------------------------- f) The gum possess centripetal acceleration ------------------------------------------------------------------------- f) The gum possess centripetal acceleration

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