and rotates through an angle of 44.9 rad. The baseball has a radius of 3.67 cm a

Question

and rotates through an angle of 44.9 rad. The baseball has a radius of 3.67 cm and is rotating about an axis as it travels, much like the earth does. What is the tangential speed of a point on the "equator" of the basebal? X m/s points I1 CJ10 8 P047 A planet orbits a star once every 2.90 x 10 s in a nearly circular orbit of radius 1.37 x 101l m. (a) With respect to the star, determine the angular speed of the planet. rad/s (b) With respect to the star, determine the tangential speed of the planet. m/s (c) With respect to the star, determine the magnitude and direction of the planet's centripetal acceleration. magnitude 0.002 m/s2 Additional Materials section 8.5 15

Explanation / Answer

given base ball pitcher

throws baseball horizontally, with speed, u = 42.5 m/s

d = 16.7 m ( horizontal distance)

angle of rotation, phi = 44.9 rad

radius r = 3.67 cm

tangential speed of a point on the equator of the baseball = v

v = u +- wr

now, time of flight = t

hence

u*t = d

t = d/u = 0.3929411764 s

hence, w = phi/t = 114.26646 rad/s

hence

where wr is tangential speed

wr = 4.193579341317 m/s

given

R = 1.37*10^11 m

T = 2.90*10^7 s

c. centripital acceleration = v^2/r

v = 2*pi*r/T

hence

ac = 4*pi^2*r^2/r*T^2 = 4*pi^2*r/T^2

ac = 0.00643108586420567006316 m/s/s = 6.4310858642 mm/s/s

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