Question

answer 1 2 and 3

001 10.0 points A car accelerates uniformly from rest and reaches a speed of 17.4 m/s in 14.1 s. The diameter of a tire is 85.4 cm Find the number of revolutions the tire makes during this motion, assuming no slip- ping. Answer in units of rev. 002 10.0 points A figure skater begins spinning counterclock- wise at an angular speed of 4.5 π rad/s. Dur- ing a 4.6 s interval, she slowly pulls her arms inward and finally spins at 7.8 T rad/s. What is her average angular acceleration during this time interval? Answer in units of rad/s2. 003 10.0 points Earth orbits the sun once every 365.25 days. Find the average angular speed of Earth about the sun Answer in units of rad/s.

Answer 1

1)

Using equation of the motion

  w=w0+At ....1

here w angular speed , w0 =0 initial angular speed. t=14.1 s

A=a/r. a=v/t =17.4/14.1 =1.234 m/s^2. ,r=85.4/2 =42.7cm

r=0.427 m

A=1.234/0.427 =2.89 rad/s^2

so. w=0+2.89×14.1

w=40.749 rad /s

Since 2π rad =1rev

So 40.749 rad =40.749/2π

=6.485 rev . Answer

2)

average angular acceleration A= w2-w1/t2-t1 . ...1

. Here w2=7.8π rad/s. w1=4.5π rad /s t2-t1=4.6 s

put these values in equation 1

. A=7.8π-4.5π/(4.6)

A=3.3×π/4.6

A=2.254 rad /s answer

3)

angular displacement of the earth =2π rad

time period. T= 365.25×24×60×60=31557600 s

average angular speed =2π/T

w=2π/31557600

W=1.99×10^(-7) rad /s