Question

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 $r_{1} and r_{2}$ 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 $( \frac{w_1}{w_2})$ is
{answer should come one}

3) The angular speed of a flywheel rotating at 90 r.p.m. is
{answer should come 3$\pi$ 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 $\pi^{2} m/s^{2}$}

Answer 1

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 

Answer 2

Answer:

12:1

Explanation:

The hour hand of a clock covers 30 degree in 60 min or 0.5

Minute hand of a clock covers 360 degree in 60 min or 6

Ratio of the angular speed of the hour to the minute hand =0.5/6

=1:12