Thread: 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

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

Sounds like a simple pendulum. Note that the speed of point P is going to be $\displaystyle v = L ~ \frac{d \theta }{dt} = L~sin(\theta)$. 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