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RPM to Radians

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A turntable rotates counterclockwise at 78 rpm. A speck of dust on the turntable is at 0.44 rad at t=0 ,What is the angle of the speck at t = 7.9 s? Your answer should be between 0 and 2π rad.

Convert rpm in radians

ω = 78rpm

= 78*2π/60s

= 8.164 rad/s

angular displacement when t = 7.9s

θ = 8.164 rad/s * 7.9  = 64.49 rad

64.49 + .44= 64.93

64.93/2π

=10.33 revolutions

remove the full number of revolutions.

=.33

=.33 x 2π

=2.07 or 2.1 radians

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