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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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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
Transcribed Image Text: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 r˙=4t m/s

angular velocity of disc θ˙=6 rad/s

radial position of block at t=1sec

r=ut+12r¨t2r¨=dr˙dt=4m/s2u=0,  t=1sr=2m

now we know that velocity 

v = r˙r^+rθ˙θ^where r^=icosθ+jsinθθ^=-isinθ+jcosθ

at t=1sec,   r˙=4 m/s  

v=4r^+2×6θ^v=42+122=16+144=410m/s

thus velocity of block at t=1sec,  =410 m/s

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