Year 12s: what will be the first way you research your future options? >>

As radians question

An oar of length L metres has the tips of its handle and its blade at A and B respectively. It is pivoted at P a quarter of the way from A to B.

During a stroke, A travels along an arc of a circle of length L/3 m.

a) Find the area of the sector swept out by PB during this stroke.

I have no idea how to get started,what would the diagram look like?

Reply 1

gooner1010

Why would p be the centre? I thought a would be the centre because its the tip and b and p would be a point on the circumference?

Reply 2

old_engineer

The diagram should look like two sectors of different size, arranged point to point, a bit like an asymmetric bow tie. The smaller sector, representing the motion of A, has centre P, radius L/4 and arc length (measured round the curve) L/3. The larger sector, representing the motion of B, has the same centre, P, and has radius 3L/4.

Reply 3

old_engineer

Original post by gooner1010

Why would p be the centre? I thought a would be the centre because its the tip and b and p would be a point on the circumference?

P is the centre because it is the pivot point, i.e. it is the point on the oar that doesn't move.

Reply 4

gooner1010

Original post by old_engineer

I honestly don't understand how that would look like in a circle :s-smilie:

Reply 5

anosmianAcrimony

Original post by gooner1010

Why would p be the centre? I thought a would be the centre because its the tip and b and p would be a point on the circumference?

An oar doesn't pivot around the tip of its handle. It pivots around an oarlock set into the edge of the boat, which is somewhere along the shaft - I guess that's what they're calling P.