The angular position of a rod varies as 20.7t2 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 = 32 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.) ____ rad/s (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.) ____ rad/s2 (c) What are the tangential speeds of the beads (in m/s) at t = 3 s? vt, 1 =____m/s
The angular position of a rod varies as 20.7t2 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 = 32 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.) ____ rad/s (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.) ____ rad/s2 (c) What are the tangential speeds of the beads (in m/s) at t = 3 s? vt, 1 =____m/s
The angular position of a rod varies as 20.7t2 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 = 32 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.) ____ rad/s (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.) ____ rad/s2 (c) What are the tangential speeds of the beads (in m/s) at t = 3 s? vt, 1 =____m/s
The angular position of a rod varies as 20.7t2 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 = 32 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.) ____ rad/s
(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.) ____ rad/s2
(c) What are the tangential speeds of the beads (in m/s) at t = 3 s? vt, 1 =____m/s vt, 2 =____m/s
(d)What are the tangential accelerations of the beads at t = 3 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 = 3 s? (Enter the magnitudes in m/s2.) ac, 1 = ______ m/s2 ac, 2 = ______ m/s2
Transcribed Image Text:(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.)
rad/s
(b) What is the angular acceleration (in rad/s) of the rod at t = 3 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 = 3 s?
Vt, 1 =
m/s
Vt, 2 =
m/s
(d) What are the tangential accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s.)
t, 1 =
m/s2
at, 2 =
m/s?
(e) What are the centripetal accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.)
ac, 1
m/s2
ac, 2
m/s2
Transcribed Image Text:The angular position of a rod varies as 20.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r, = 13 cm from the rotation axis and the
other at r, = 32 cm from the rotation axis. (Note: figure may not be drawn to scale.)
Counterclockwise rotation
Axis of rotation
13 cm
32 cm
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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