lowest point? 60 A centripetal-acceleration addict rides in uniform circular mot

Question

lowest point? 60 A centripetal-acceleration addict rides in uniform circular motion with period T- 2.0 s and radiusr3.00 m. At f, his accel- eration is a(6.00 m/si(-4.00 m/s)j. At that instant, what are the values of (a) V.a and (b) xa? 61 When a large star becomes a supernova, its core may be com- pressed so tightly that it becomes a neutron star, with a radius of about 20 km (about the size of the San Francisco area). If a neutron star rotates once every second, (a) what is the speed of a particle on the star's equator and (b) what is the magnitude of the particle's cen- tripetal acceleration? (c) If the neutron star rotates faster, do the an- swers to (a) and (b) increase, decrease, or remain the same? 62 What is the magnitude of the acceleration of a sprinter run- ning at 10 m/s when rounding a turn of radius 25 m? 63 At 2.00s, the acceleration of a particle in counter- clockwise circular motion is (6.00 m/s2)1 + (4.00 m/s2j. It moves at constant speed. At time 12-5.00s, the particle's acceleration is (4.00 m/s?)i (-6.00 m/s2). What is the radius of the path taken by the particle if t2-t is less than one period? 4A particle moves horizontally in uniform circular motión, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of -5.00î m/s and an acceleration of +12.5j m/s2. What are the (a) x and (b) y coordinates of the center of the circular path?

Explanation / Answer

64.

From the given informations

Particle is traveling to the left and acceleration is upward.

ac = +12.5 j

v = -5 i

Centripetal acceleration is given by

ac = v^2/r

r = v^2/ac = 5^2/12.5

r = 2 m

Since acceleration is in y-axis, So center will be directly above the point (4.00, 4.00)

Since no acceleration in x-direction, So

x coordinate of center of circular path = 4.00 m

And

y coordinate of center of circular path = 4.00 m + radius = 4.00 + 2.00 = 6.00 m

Center = (4.00 m, 6.00 m)

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