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 bicycle wheel 67.0 [cm] in diameter rotates about its central axis with a constant angular acceleration of 4.48 [rad/s2]. It starts from rest at time t =0 [s], and a reference point on the wheel's rim P makes an angle of 60.0° above the horizontal at this time. When the wheel starts rotating, at time t=3.70 [s],
A. what is the magnitude of the tangential acceleration of the wheel's rim?
B. what is the angular speed of the wheel's rim?
C. what is the tangential speed of the wheel's rim?
D. what is point P's new angular position from the horizontal in radians?
At t=1.50 [s], a small, 92.5 [g] pebble got stuck on the rim of the wheel.
E. What is the pebble's moment of inertia with respect to the wheel's axis of rotation?
F. At t=3.70 [s], what is the pebble's rotational kinetic energy?
The radial position r of a particle's path is defined
by an equation, r = 5∙ cos (20) m. At the initial
time, the angular position is 0 = 0° if the angular
velocity of the particle is w= 3t² rad/sec, where
It is in seconds, calculate the value of the
e-component of acceleration at the instant 0 = 30° in
m/sec².
A disk of radius 3.00 m rotates like a merry-go-round as given by the function θ = 2.00t^4 + 6.00t^2, where θ is in radians and t is in seconds. What is the radial acceleration (m/s2) of a point on the rim t = 2.00 s?
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