(a) What is the tangential acceleration of a bug on the rim of a 8.0 in. diamete

Question

(a) What is the tangential acceleration of a bug on the rim of a 8.0 in. diameter disk if the disk moves from rest to an angular speed of 80 rev/min in 5.0 s?
_______________________m/s2

(b) When the disk is at its final speed, what is the tangential velocity of the bug?
_______________________m/s

(c) One second after the bug starts from rest, what is its tangential acceleration?
_______________________m/s2
What is its centripetal acceleration?
______________________ m/s2
What is its total acceleration?
______________________ m/s2
______________________° (relative to the tangential acceleration)

Explanation / Answer

( a )

= 0 + t ;

0 = 80 * 2 / 60   +   * 5 ;

or = 1.6755 rad / s ^2 ;

a = r = 1.6755 * ( 8/2 * 2.54 e-2 )          since    1 in = 2.54 e -2 m ;

a = 0.170232 m / s^2 ;

( b )

v = r = ( 80 * 2 / 60 ) ( 8/2 * 2.54 e-2 ) = 0.85116 m /s

( c )

tangential accn = 0.170232 ,m / s^2    as calculated in ( a )

v = at = 0.170232 * 1 = 0.170232 m /s ;

centripetal accn = v^2 / r = 0.170232^2 / ( 4 * 2.54 e-2 ) = 0.2852 m /s ^2 ;

total acceleration = ( 0.2842^2 + 0.170232 ^2 ) = 0.33128 m /s^2   

= tan inv ( 0.2852 / 0.170232 ) = 59.1675 d3egreee

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