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1) The ratio of the angular speeds of the hour hand and the minute hand of a clock is

{answer should come 1:12}

2) Two particles A and B move in concentric circles of radii respectively in such a way that A, B and the centre of the circle (O) always lie on a straight line. The ratio of their angular velocities is {answer should come one}

3) The angular speed of a flywheel rotating at 90 r.p.m. is {answer should come 3 rad/s}

4) A flywheel of diameter 1 m is rotation at 600 r.p.m. The acceleration of a point on the rim of the fly wheel is {answer should come 200 }

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The hours hand rotates full circle in 12 hours. So it covers an angle 360⁰ in 12 hours. Minutes hand covers a full circle in 12 hrs.

angular velocity of hours hand = 2π/(12*3600) radians/sec angular velocity of minutes hand = 2π/3600 radians / sec so ratio = 1 : 12

2) see diagram. The two particles are in a straight line always. It means they cover the same angle θ in same time duration. so angular velocities are ω1 = θ/time = ω2 so ω1 = ω2

3) angular speed or velocity = angle / time = 90 * 2 π / 60 = 3π rad/sec

4) angular velocity of the point = angle / time = 600 * 2π / 60 = 20 π rad/sec centripetal acceleration towards the center of circle = r ω² = 0.5 * (20π)² rad/sec² = 200π² rad/sec² = 1973.92 rad/sec²