A small block slides out along the slot in the disk with a speed of † = 4t m/s ( t is in seconds) The disk rotates at a constant rate of 6 rad/s. If the block starts from rest at the origin, determine the magnitudes of its velocity and acceleration when t = 1 s. 0 = 6 rad/s

A small block slides out along the slot in the disk with a speed of † = 4t m/s ( t is in seconds) The disk rotates at a constant rate of 6 rad/s. If the block starts from rest at the origin, determine the magnitudes of its velocity and acceleration when t = 1 s. 0 = 6 rad/s

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Question

Please help with the attached problem.

CYLINDRICAL
1) A small block slides out along the slot in the disk with a speed of i = 4t
m/s (t is in seconds) The disk rotates at a constant rate of 6 rad/s. If the
block starts from rest at the origin, determine the magnitudes of its velocity
and acceleration when t = 1 s.
e = 6 rad/s

Expert Solution

Step 1 velocity

we are given radial velocity of block $\dot{r} = 4 t m / s$

angular velocity of disc $\dot{θ} = 6 r a d / s$

radial position of block at t=1sec

$r = u t + \frac{1}{2} \ddot{r} t^{2} \ddot{r} = \frac{d \dot{r}}{d t} = 4 m / s^{2} u = 0, t = 1 s r = 2 m$

now we know that velocity

$v = \dot{r} \hat{r} + r \dot{θ} \hat{θ} w h e r e \hat{r} = i \cos θ + j \sin θ \hat{θ} = - i \sin θ + j \cos θ$

at t=1sec, $\dot{r} = 4 m / s$

$v = 4 \hat{r} + 2 \times 6 \hat{θ} |v| = \sqrt{4^{2} + 12^{2}} = \sqrt{16 + 144} = 4 \sqrt{10} m / s$

thus velocity of block at t=1sec, = $4 \sqrt{10}$ m/s

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