Question

Please answer both 2 and 5.

3-2 What is the angular speed, in SI units, of: 5 pts (a) The earth in its orbit about the sun every 365 days. rad/s ( + 2E-9 rad/s) (b) The moon in its orbit about the earth every 27.3 days. rad/s ( + 6E-8 rad/s) 3-5 A car is traveling at 96.0 km/hr The tires have a radius R = 38.4 cm. 5 pts (a) What is the angular speed of the tire (in SI units)? rad/s ( + 0.2 rad/s) (b) What is the centripetal acceleration of a piece of tire on the outer edge? m/s( + 20 m/s2)

Answer 1

3-2)a earth orbits around the sun in 365 days;

time period T = 365 days

T = 365 x 24 x 60 x 60 sec

T = 31536000 sec

We know the Earth goes round the Sun, all the way around is 2$\pi$ radians (360 degrees)

so anglular speed is

-

w = 21 31536000

w = 1.9924 x 10- rad/s

(b) moon orbits around the earth in 27.3 days;

time period T = 27.3 days

T = 27.3 x 24 x 60 x 60 sec

T = 2358720 sec

We know the moon goes round the earth, all the way around is 2$\pi$ radians (360 degrees)

so anglular speed is

-

2π u = 9258720

w = 2.66 x 10-6 rad/s

......................................................................................

3-5a) speed of car v = 96 km/h = 26.67 m/s

radius of tire r = 38.4 cm = 0.384 m

as we know the relation between linear angular speed

v = Rw

w = v/R

w = 26.67/0.384

w = 69.45 rad/s

(b) centrepetal acceleration on tire

a = v2/R

a = 26.672/0.384

a = 1852.314 m/s2