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tomcell

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Hi this is some coursework i have for an assignment is there anyway you could shed some light on what steps to take?

So far i have worked out the inertia with the children to be 552 by working out the mass of the roundabout to be 200KGS plus the weight of the children and using 0.5mv^2, not sure where yo go from here but i will post more info later but am posting this from my phone so will be more helpful later. thanks

Figure 3 shows a plan view of an object, that is, the view looking down on the object from directly overhead.

The object is a children’s roundabout which is free to rotate about a vertical axle through its centre. The axle is shown by the small circle in the centre of Figure 3.

Figure 3 For use with Question 4.

The roundabout has a radius of 2.0 m and a moment of inertia about the central axle of 400 kg m2. Four children, each of mass 19 kg, then stand on the roundabout, each at a distance 1.9 m from its centre. The children are equally spaced, that is, the angular separation of one child from the next is 90°. For the purposes of this question you should treat each child as a point mass. Ignore friction between the roundabout and the axle and any effects due to air resistance.

(a) What is the relationship between the total external torque acting on a body and the rate of change of the body’s angular momentum? Under what conditions does the angular momentum of a body remain constant in time?

(b)

The roundabout is initially at rest with all the children on it, and a constant force F of magnitude 94 N is appliedtangentially at the rim of the roundabout, as shown in Figure 3, for 5.0 s. Find the following quantities for

the roundabout at the end of this time:

(i) the magnitude of the angular momentum,

(ii) the direction of the angular momentum,

(iii) the angular speed,

(iv) the rotational energy.

(c)

At the end of this interval, i.e. at t = 5.0 s, the force F ceases to act, and at the same time each child moves radially inwards to a new position 20 cm from the axle. Find the following quantities for the roundabout:

(i)

the new magnitude of angular momentum, (1 mark)

(ii)

the new angular speed, (3 marks)

(iii) the new rotational energy. (1 mark)

(d)

A constant frictional retarding force of 94 N is now applied to the outer edge of the roundabout. How long will it take for this force to bring the roundabout to rest?

(e)

Comment on the relationship between the time that you obtained in part (d) and the time that the force acted in (b). Interpret this relationship in terms of the torque acting and the rate of change of a rotational quantity (angular speed, angular momentum or rotational energy)

]

So far i have worked out the inertia with the children to be 552 by working out the mass of the roundabout to be 200KGS plus the weight of the children and using 0.5mv^2, not sure where yo go from here but i will post more info later but am posting this from my phone so will be more helpful later. thanks

Figure 3 shows a plan view of an object, that is, the view looking down on the object from directly overhead.

The object is a children’s roundabout which is free to rotate about a vertical axle through its centre. The axle is shown by the small circle in the centre of Figure 3.

Figure 3 For use with Question 4.

The roundabout has a radius of 2.0 m and a moment of inertia about the central axle of 400 kg m2. Four children, each of mass 19 kg, then stand on the roundabout, each at a distance 1.9 m from its centre. The children are equally spaced, that is, the angular separation of one child from the next is 90°. For the purposes of this question you should treat each child as a point mass. Ignore friction between the roundabout and the axle and any effects due to air resistance.

(a) What is the relationship between the total external torque acting on a body and the rate of change of the body’s angular momentum? Under what conditions does the angular momentum of a body remain constant in time?

(b)

The roundabout is initially at rest with all the children on it, and a constant force F of magnitude 94 N is appliedtangentially at the rim of the roundabout, as shown in Figure 3, for 5.0 s. Find the following quantities for

the roundabout at the end of this time:

(i) the magnitude of the angular momentum,

(ii) the direction of the angular momentum,

(iii) the angular speed,

(iv) the rotational energy.

(c)

At the end of this interval, i.e. at t = 5.0 s, the force F ceases to act, and at the same time each child moves radially inwards to a new position 20 cm from the axle. Find the following quantities for the roundabout:

(i)

the new magnitude of angular momentum, (1 mark)

(ii)

the new angular speed, (3 marks)

(iii) the new rotational energy. (1 mark)

(d)

A constant frictional retarding force of 94 N is now applied to the outer edge of the roundabout. How long will it take for this force to bring the roundabout to rest?

(e)

Comment on the relationship between the time that you obtained in part (d) and the time that the force acted in (b). Interpret this relationship in terms of the torque acting and the rate of change of a rotational quantity (angular speed, angular momentum or rotational energy)

]

## The Attempt at a Solution

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