Question

Pin p is constrained to move along the curve defined by the lemniscate r=(4sin2θ)ft.if the slotted arm oa rotates counterclockwise with a constant angular velocity of θ˙ = 1.0 rad/s , determine the magnitude of the velocity of peg p when θ = 59 ∘.

Answer 1

position of the peg is given by the equation

$r = 4 sin2\theta$

now the rate of change in position is given as

$v = \frac{dr}{dt}$

$v = \frac{d}{dt}(4 sin2\theta)$

$v = 8cos2\theta*\frac{d\theta}{dt}$

$v = 8 cos2\theta*\omega$

given that

$\omega = 1 rad/s$

$\theta = 59 degree$

now we have

$v = 8*cos(2*59)* 1 = -3.76 m/s$

so its speed will be 3.76 m/s in magnitude