CALC At t = 0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by θ ( t ) = (250 rad/s) t − (20.0 rad/s 2 ) t 2 − (1.50 rad/s 3 ) t 3 . (a) At what time is the angular velocity of the motor shaft zero? (b) Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity, (c) How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero? (d) How fast was the motor shaft rotating at t = 0, when the current was reversed? (e) Calculate the average angular velocity for the time period from t = 0 to the time calculated in part (a).
CALC At t = 0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by θ ( t ) = (250 rad/s) t − (20.0 rad/s 2 ) t 2 − (1.50 rad/s 3 ) t 3 . (a) At what time is the angular velocity of the motor shaft zero? (b) Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity, (c) How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero? (d) How fast was the motor shaft rotating at t = 0, when the current was reversed? (e) Calculate the average angular velocity for the time period from t = 0 to the time calculated in part (a).
CALC At t = 0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by θ(t) = (250 rad/s)t − (20.0 rad/s2)t2 − (1.50 rad/s3) t3. (a) At what time is the angular velocity of the motor shaft zero? (b) Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity, (c) How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero? (d) How fast was the motor shaft rotating at t = 0, when the current was reversed? (e) Calculate the average angular velocity for the time period from t = 0 to the time calculated in part (a).
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 .
At t = 0s a grinding wheel has an angular velocity of 24.0 rad/s. It has a constant angular acceleration of 30.0 rad/s2 until a circuit breaker trips at t = 2.3 s. From then on it coasts to a stop over the next 10.0 seconds at constant angular acceleration.
Through what total angle did the grinding wheel rotate? (Give your answer in radians.)
The angular position of a point on the rim of a rotating wheel is given by 0 = 7.36t - 5.00+2 + 3.1113, where O is in radians and t is in
seconds. What are the angular velocities at (a) t = 2.31 s and (b) t = 6.20 s? (c) What is the average angular acceleration for the time
interval that begins at t = 2.31 s and ends at t = 6.20 ? What are the instantaneous angular accelerations at (d) the beginning and (e)
the end of this time interval?
Only need help with D E part of problem
The angular position of an object that rotates about a fixed axis is given by θ(t) = θ0 eβt, where β = 4 s−1, θ0 = 0.9 rad, and t is in seconds.
What is the magnitude of the total linear acceleration at t = 0 of a point on the object that is 2.1 cm from the axis?
Answer in units of cm/s2.
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