# Further Maths

• Dec 7th 2013, 03:05 AM
notorious96
Further Maths
A line OP of ﬁxed length L rotates in a plane about the ﬁxed point O. At time t = 0, the line is at the
position OA. At time t, angle AOP = θ radians and dθ/dt= sin θ. Show that, for all t, the magnitude of
the acceleration of P is equal to the magnitude of its velocity.

hey guys could you please explain the concept behind this question and the solution too. Greatly appreciate it.

Thanks :D
• Dec 7th 2013, 05:56 AM
topsquark
Re: Further Maths
Quote:

Originally Posted by notorious96
A line OP of ﬁxed length L rotates in a plane about the ﬁxed point O. At time t = 0, the line is at the
position OA. At time t, angle AOP = θ radians and dθ/dt= sin θ. Show that, for all t, the magnitude of
the acceleration of P is equal to the magnitude of its velocity.

hey guys could you please explain the concept behind this question and the solution too. Greatly appreciate it.

Thanks :D

Sounds like a simple pendulum. Note that the speed of point P is going to be $v = L ~ \frac{d \theta }{dt} = L~sin(\theta)$. The tangential acceleration will be the component of the overall force (pointing down through the whole swing) acting in the direction of the velocity. So how do you calculate this?

-Dan