a) Find radius of a wheel such that an arc length of 1.8 m on its rim correspond

Question

a) Find radius of a wheel such that an arc length of 1.8 m on its rim corresponds to an angle of 0.61 rad. _____ m

a) Find radius of a wheel such that an arc length of 1.8 m on its rim corresponds to an angle of 0.61 rad. _____ m

b) What is the angular displacement in radians of the Earth around the Sun in one hour? It takes exactly 365 days in the counterclockwise direction, as viewed from above the North Pole. ____ rad c) With an angular velocity of 2.8 rad/s, how much time is required to complete 16 complete revolutions?
_____sec

Explanation / Answer

a)

given,

arc length l=1.8 m

angular displacement theta=(0.61*pi) rad

now,

radius of the wheel is, r=l/theta

r=1.8/(0.61*pi)

=0.94 m

b)

here,

angular velocity of the earth is,

w=angular dispalcement/time

=(2*pi) rad/(365*24) hr

=[2*pi/(365*24)] rad/hr

now,

angular dispalcement of the earth in 1hr is,

theta =w*t

=([2*pi/(365*24)]rad/hr)*1hr

=[2*pi/(365*24)] rad

=7.17*10^-4 rad

=0.00072 rad

c)

w=angular dispalcement/time

t=angular dispalcement/w

=16rev/(2.8*pi)

=(16*2pi)/(2.8*pi)

=11.43 sec

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