Question

A bicyclist starting at rest produces a constant angular
acceleration of 1.10 rad/s^{2} for wheels that are 37.5 cm
in radius.

HINT

(a)

What is the bicycle's linear acceleration (in m/s^{2})?
(Enter the magnitude.)

m/s^{2}

(b)

What is the angular speed of the wheels (in rad/s) when the bicyclist reaches 10.6 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

a) Linear acceleration

where r is the radius =37.5 cm=0.375m

linear acceleration= 1.10*0.375 m/s2=0.41m/s2

b) Linear velocity (v)=10.6 m/s ; using the formula

now angular velocity=v/r=10.6/0.375=28.26 sec-1

c) now let time taken to reach v=10.6 m/s is t sec ,initial velocity u=0 m/s

using v=u+at ; t=v/a=10.6/0.41 s=25.85 sec

using and =28.26*25.85=730.5 deg=12.74 radians

d) Distance travelled(s)= 1/2 *a*t2 as u=0

so s=0.5*0.41*(25.85)2 =136.9 m

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