The angle an airplane propeller makes with the horizontal as a function of time is given by θ = (125rad/s) t + (42.5rad/s 2 ) t 2 . (a) Estimate the instantaneous angular velocity at t = 0.00 by calculating the average angular velocity from t = 0.00 to t = 0.010s. (b) Estimate the instantaneous angular velocity at t = 1.000 s by calculating the average angular velocity from t = 1.000 s to t = 1.010 s. (c) Estimate the instantaneous angular velocity at t = 2.000 s by calculating the average angular velocity from t = 2.000s to t = 2.010s. (d) Based on your results from parts (a), (b), and (c), is the angular acceleration of the propeller positive, negative or zero? Explain, (e) Calculate the average angular acceleration from t = 0.00 to t = 1.00s and from t = 1.00s to t = 2.00 s.
The angle an airplane propeller makes with the horizontal as a function of time is given by θ = (125rad/s) t + (42.5rad/s 2 ) t 2 . (a) Estimate the instantaneous angular velocity at t = 0.00 by calculating the average angular velocity from t = 0.00 to t = 0.010s. (b) Estimate the instantaneous angular velocity at t = 1.000 s by calculating the average angular velocity from t = 1.000 s to t = 1.010 s. (c) Estimate the instantaneous angular velocity at t = 2.000 s by calculating the average angular velocity from t = 2.000s to t = 2.010s. (d) Based on your results from parts (a), (b), and (c), is the angular acceleration of the propeller positive, negative or zero? Explain, (e) Calculate the average angular acceleration from t = 0.00 to t = 1.00s and from t = 1.00s to t = 2.00 s.
The angle an airplane propeller makes with the horizontal as a function of time is given by θ = (125rad/s)t + (42.5rad/s2)t2. (a) Estimate the instantaneous angular velocity at t = 0.00 by calculating the average angular velocity from t = 0.00 to t = 0.010s. (b) Estimate the instantaneous angular velocity at t = 1.000 s by calculating the average angular velocity from t = 1.000 s to t = 1.010 s. (c) Estimate the instantaneous angular velocity at t = 2.000 s by calculating the average angular velocity from t = 2.000s to t = 2.010s. (d) Based on your results from parts (a), (b), and (c), is the angular acceleration of the propeller positive, negative or zero? Explain, (e) Calculate the average angular acceleration from t = 0.00 to t = 1.00s and from t = 1.00s to t = 2.00 s.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
A pendulum has a 0.4-m-long cord and is given a tangential velocity of 0.2 m/s toward the
vertical from a position 0 = 0.3 rad.
Part A
Determine the equation which describes the angular motion.
Express your answer in terms of the variable t. Express coefficients in radians to three significant figures.
ΜΕ ΑΣΦ
vec
(t)=0.3 cos (4.95t) + 0.101 sin (4.95t)
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Part A
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The uniform 150-lb stone (rectangular block) is being turned over on its side by pulling the
vertical cable slowly upward until the stone begins to tip.
(Figure 1)
If it then falls freely (T = 0) from an essentially balanced at-rest position, determine the speed at which the corner A strikes the pad at B. The stone does not slip at its corner C as it falls. Suppose that height of the stone is
L = 1.2 ft.
Express your answer to three significant figures and include the appropriate units.
?
ft
VA 10.76
S
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Consider the circuit shown in the figure. The battery has emf ε = 69 volts and negligible internal resistance. The inductance is L = 0.4 H and the resistances are R 1 = 12 Ω and R 2 = 9.0 Ω. Initially the switch S is open and no currents flow. Then the switch is closed. After leaving the switch closed for a very long time, it is opened again. Just after it is opened, what is the current in R 1?
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