The angular position of a rod varies as 19.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 13 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 = 3 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) (b) What is the angular acceleration (in rad/s2) of the rod at t = 3 s? (Indicate the direction with the sign of your answer.) (c) What are the tangential speeds of the beads (in m/s) at t = 3 s? (d) What are the tangential accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.) (e) What are the centripetal accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.)
The angular position of a rod varies as 19.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 13 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 = 3 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) (b) What is the angular acceleration (in rad/s2) of the rod at t = 3 s? (Indicate the direction with the sign of your answer.) (c) What are the tangential speeds of the beads (in m/s) at t = 3 s? (d) What are the tangential accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.) (e) What are the centripetal accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.)
The angular position of a rod varies as 19.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 13 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 = 3 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) (b) What is the angular acceleration (in rad/s2) of the rod at t = 3 s? (Indicate the direction with the sign of your answer.) (c) What are the tangential speeds of the beads (in m/s) at t = 3 s? (d) What are the tangential accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.) (e) What are the centripetal accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.)
The angular position of a rod varies as 19.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 13 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 = 3 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.)
(b) What is the angular acceleration (in rad/s2) of the rod at
t = 3 s? (Indicate the direction with the sign of your answer.)
(c) What are the tangential speeds of the beads (in m/s) at
t = 3 s?
(d) What are the tangential accelerations of the beads at
t = 3 s? (Enter the magnitudes in m/s2.)
(e) What are the centripetal accelerations of the beads at
t = 3 s? (Enter the magnitudes in m/s2.)
Transcribed Image Text:Counterclockwise rotation
Axis of rotation
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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