The angular position of a rod varies as 23.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 15 cm from the rotation axis and the other at r2 = 42 cm from the rotation axis. (Note: figure may not be drawn to scale.) (a) What is the instantaneous angular velocity (in rad/s) of the rod at t = 7 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) rad/s (b) What is the angular acceleration (in rad/s2) of the rod at t = 7 s? (Indicate the direction with the sign of your answer.) rad/s2 (c) What are the tangential speeds of the beads (in m/s) at t = 7 s?
The angular position of a rod varies as 23.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 15 cm from the rotation axis and the other at r2 = 42 cm from the rotation axis. (Note: figure may not be drawn to scale.) (a) What is the instantaneous angular velocity (in rad/s) of the rod at t = 7 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) rad/s (b) What is the angular acceleration (in rad/s2) of the rod at t = 7 s? (Indicate the direction with the sign of your answer.) rad/s2 (c) What are the tangential speeds of the beads (in m/s) at t = 7 s?
The angular position of a rod varies as 23.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 15 cm from the rotation axis and the other at r2 = 42 cm from the rotation axis. (Note: figure may not be drawn to scale.) (a) What is the instantaneous angular velocity (in rad/s) of the rod at t = 7 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) rad/s (b) What is the angular acceleration (in rad/s2) of the rod at t = 7 s? (Indicate the direction with the sign of your answer.) rad/s2 (c) What are the tangential speeds of the beads (in m/s) at t = 7 s?
The angular position of a rod varies as 23.7t2 radians from time
t = 0. The rod has two beads on it as shown in the following figure, one at
r1 = 15 cm from the rotation axis and the other at r2 = 42 cm from the rotation axis. (Note: figure may not be drawn to scale.)
(a) What is the instantaneous angular velocity (in rad/s) of the rod at
t = 7 s?
(Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.)
rad/s
(b) What is the angular acceleration (in rad/s2) of the rod at
t = 7 s?
(Indicate the direction with the sign of your answer.)
rad/s2
(c) What are the tangential speeds of the beads (in m/s) at
t = 7 s?
vt, 1
= m/s
vt, 2
= m/s
(d) What are the tangential accelerations of the beads at
t = 7 s?
(Enter the magnitudes in m/s2.)
at, 1
= m/s2
at, 2
= m/s2
(e) What are the centripetal accelerations of the beads at
t = 7 s?
(Enter the magnitudes in m/s2.)
ac, 1
= m/s2
ac, 2
= m/s2
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 .
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