$2.(10$ points$)$ When a large star becomes a supernova, its core may be compressed 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 centripetal acceleration? $($c$)$ If the neutron star rotates faster, do the answers to $($a$)$ and $($b$)$ increase, decrease, or remain the same?

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