At t = 0, a flywheel has an angular velocity of 4.7 rad/s, a constant angular acceleration of −0.25 rad/s 2 , and a reference line at θ 0 = 0. (a) Through what maximum angle θ max will the reference line turn in the positive direction? What are the (b) first and (c) second times the reference line will be at θ = 1 2 θ max ? At what (d) negative time and (e) positive time will the reference line be at θ = 10.5 rad? (f) Graph θ versus t , and indicate your answers.
At t = 0, a flywheel has an angular velocity of 4.7 rad/s, a constant angular acceleration of −0.25 rad/s 2 , and a reference line at θ 0 = 0. (a) Through what maximum angle θ max will the reference line turn in the positive direction? What are the (b) first and (c) second times the reference line will be at θ = 1 2 θ max ? At what (d) negative time and (e) positive time will the reference line be at θ = 10.5 rad? (f) Graph θ versus t , and indicate your answers.
At t = 0, a flywheel has an angular velocity of 4.7 rad/s, a constant angular acceleration of −0.25 rad/s2, and a reference line at θ0 = 0. (a) Through what maximum angle θmax will the reference line turn in the positive direction? What are the (b) first and (c) second times the reference line will be at
θ
=
1
2
θ
max
? At what (d) negative time and (e) positive time will the reference line be at θ = 10.5 rad? (f) Graph θ versus t, and indicate your answers.
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 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 28 m/s when a 60 kg skydiver drops out by releasing his grip on the glider. What is the glider's speed just after the skydiver lets go?
PROBLEM 2
A cube of mass m is placed in a rotating funnel.
(The funnel is rotating around the vertical axis shown
in the diagram.) There is no friction between the cube
and the funnel but the funnel is rotating at just the
right speed needed to keep the cube rotating with the
funnel. The cube travels in a circular path of radius r,
and the angle between the vertical and the wall of the
funnel is 0. Express your answers to parts (b) and (c)
in terms of m, r, g, and/or 0.
(a) Sketch a free-body diagram for the cube. Show
all the forces acting on it, and show the appropriate
coordinate system to use for this problem.
(b) What is the normal force acting on the cube?
FN=mg58
(c) What is the speed v of the cube?
(d) If the speed of the cube is different from what you
determined in part (c), a force of friction is necessary
to keep the cube from slipping in the funnel. If the
funnel is rotating slower than it was above, draw a
new free-body diagram for the cube to show which
way friction…
Circular turns of radius r in a race track are often banked at an angle θ to allow the cars to achieve higher speeds around the turns. Assume friction is not present.
Write an expression for the tan(θ) of a car going around the banked turn in terms of the car's speed v, the radius of the turn r, and g so that the car will not move up or down the incline of the turn.
tan(θ) =
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