A particle moves on a circle of fixed radius R. At an instant its net acceleration makes an angle 45° with the inward radial direction. Which statements are correct?
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Question

A particle moves on a circle of fixed radius R. At an instant its net acceleration makes an angle 45° with the inward radial direction. Which statements are correct?

G1 Physics · Accepted Answer

If the resultant acceleration makes 45° with the inward radial direction, the magnitudes of the perpendicular components are equal: |aₜ|=a_c. Thus R|α|=Rω², so |α|=ω². Also |dv/dt|=|aₜ|=v²/R. The tangential component may be along or opposite to velocity, so speed may increase or decrease; it need not be increasing.