In this worksheet, we will practice using the angular speed equation to find the acceleration of a body moving in a circular path.

**Q1: **

A clockmaker is attaching an hour hand to a clock that is hanging on a vertical wall. The hour hand has a mass of and a length of and it is attached to the clock through a point that is at a distance of from one of the ends. The clockmaker is attaching the hand so that it points at 12 oβclock. As he is trying to fix it in place, he slightly disturbs it from its position of equilibrium and it starts to rotate. Assuming that the hour hand is uniform and the axle is smooth, find the angular speed of the hour hand after it has turned through an angle of . Give your answer in terms of , , and the acceleration due to gravity .

- A
- B
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- E

**Q2: **

An aeroplane needed to change direction from a bearing of to a bearing of . It did this by banking at an angle of to the horizontal. The banking manoeuvre caused the aeroplane to travel in a horizontal circular arc so that, after 30 seconds, it was pointing in the right direction. Given that the planeβs speed was 359 km/h throughout the manoeuvre, find the two possible values of . Give your answers correct to one decimal place. Take .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q3: **

A particle of mass lies on a rotating rough disc away from its centre, where the coefficient of friction between the particle and the disc is . Given that the disc is rotating horizontally at a constant angular speed about its vertical axis and that remains at rest relative to the disc when , find . Consider the acceleration due to gravity to be .

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**Q4: **

On his way home, James came across a traffic circle of radius 18 m while driving in his car. Suppose he drove round the traffic circle at 26 km/h, determine his acceleration correct to two decimal places.

**Q5: **

A bend in a road follows a horizontal circular arc of radius 107 m. At what angle to the horizontal should the road be banked so that a car travelling at 16 km/h experiences no frictional force perpendicular to its direction of motion? Give your answer correct to one decimal place. Take .

**Q6: **

A bead of mass 55 g was threaded on a wire. The wire was bent into a circular hoop of radius 0.99 m. The bead moves around the hoop at a constant speed of 4.5 m/s. Given that the hoop lies in a horizontal plane, find the vertical component and the horizontal component of the reaction force acting on the bead due to the wire. Take .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q7: **

An athlete goes around a circular track at 3.7 m/s. If the radius of the track is 19 m, how long does one lap take? Round your answer to one decimal place.

**Q8: **

A bead of mass 155 g is attached by a light inextensible string of length 31 cm to a fixed point on the smooth horizontal surface of a table. What is the tension in the string if the bead moves at a constant speed of 14 m/s around with the string taut at all times?

**Q9: **

A particle moves in a horizontal circular path with a radius of
175 m at an acceleration of
7 m/s^{2} towards the centre.
Determine its angular speed in radians per second.