Two point masses P1 and P2 start at point A with E1.19 zero initial velocities and travel on a circular path.

Question

Two point masses P₁ and P₂ start at point A with  zero initial velocities and travel on a circular path. P₁ moves with a uniform tangential acceleration at₁ and P₂ moves with a given uniform angular velocity ω₂. 

a) What value must a_t1 have in order for the two masses to meet at point B?

b) What is the angular velocity of P₁ at B? 

c) What are the normal accelerations of the two masses at B?

Answer 1

The velocity and position of P₁ follow from a_t1 = const = v˙ with the initial conditions s₀₁ = 0 and v₀₁ = 0 as

Similarly, for point P₂ we obtain from a_t2 = 0 with s₀₂ = 0 and v₀₂ = rω₂:

v₂ = rω₂ , s₂ = rω₂t

a) Both points meet at time t_B at point B thus

This leads to

b) The tangential acceleration a_t1 and the time t_B are now known. Hence, we can calculate the angular velocity of P₁ at B

c) The normal accelerations at B follow from an = rω₂