The angle through which a disk drive turns is given by ( t )= a + b t c t 3, whe
ID: 1796044 • Letter: T
Question
The angle through which a disk drive turns is given by (t)=a+btct3, where a,b and care constants, t is in seconds, and is in radians. When t=0,=/4rad and the angular velocity is 1.70 rad/s , and when 1.30 s , the angular acceleration is 1.30 rad/s2 .
Find a including their units.
A) Find including their units.
/4rad/s
B) Find b including their units
5.3 rad/s2
C) Find c including their units
4.5 rad/s3
D) What is the angular acceleration when =/4rad?
E) What is when the angular acceleration is 4.00 rad/s2 ?
F) What is the angular velocity when the angular acceleration is 4.00 rad/s2 ?
/4rad/s2 /2rad/s /4rad/4rad/s
B) Find b including their units
1.70 rad/s2 1.70 rad/s 5.3 rad/s5.3 rad/s2
C) Find c including their units
-0.167 rad/s3 -0.167 rad/s2 3.3 rad/s34.5 rad/s3
D) What is the angular acceleration when =/4rad?
E) What is when the angular acceleration is 4.00 rad/s2 ?
F) What is the angular velocity when the angular acceleration is 4.00 rad/s2 ?
Explanation / Answer
given theta(t) = a + b*t - c*t^3
A) pi/4 rad <<<<<<<<----------------Answer
at t = 0, theta = pi/4
pi/4 = a + 0 - 0
a = pi/4
B) 1.7 rad/s <<<<<<<<----------------Answer
w = d(theta)/dt
w = b - 3*c*t^2
1.7 = b - 0
b = 1.7 rad/s
alfa = dw/dt
= -3*2*c*t
= -6*c*t
at t = 1.3 s, alfa = 1.3 rad/s^2
so,
1.3 = -6*c*1.3
==> c = -1/6
= -0.167 rad/s^3
C) -0.167 rad/s^3 <<<<<<<<----------------Answer
D) at time t = 0, theta = pi/4
alfa = -6*c*t
= 0 (since t = 0) <<<<<<<<----------------Answer
E) alfa = -3*c*t
4 = -3*(-0.167)*t
==> t = 7.98 s
at time t = 7.98 s
theta(t) = a + b*t - c*t^3
= pi/4 + 1.7*7.98 - (-0.167)*7.98^3
= 99.2 rad <<<<<<<<<<-----------------Answer
F)
w = b - 3*c*t^2
= 1.7 - 3*(-0.167)*7.98^2
= 33.6 rad/s <<<<<<<<<<-----------------Answer
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