Question

A bicyclist starting at rest produces a constant angular acceleration of 1.10 rad/s² for wheels that are 37.5 cm in radius.

HINT

(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 10.6 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