Open Question
The angular velocity of a process control motor is ω = ( 20 ─ ½ t² ) rad/s, where t is in seconds.b. Through what angle does the motor turn between t = 0 s and the instant at which it reverses direction?
12. Rotational Kinematics
Rotational Velocity & Acceleration
Back12. Rotational Kinematics
Rotational Velocity & Acceleration
- Open QuestionA painted tooth on a spinning gear has angular position θ = (6.0 rad/s⁴)t⁴. What is the tooth's angular acceleration at the end of 10 revolutions?
- Open QuestionA 6.0-cm-diameter gear rotates with angular velocity ω = ( 20 ─ ½ t² ) rad/s where t is in seconds. At t = 4.0 s, what are:b. The tangential acceleration of a tooth on the gear?
- Open QuestionA 6.0-cm-diameter gear rotates with angular velocity ω = ( 20 ─ ½ t² ) rad/s where t is in seconds. At t = 4.0 s, what are:a. The gear's angular acceleration?
- Open QuestionCALC A fan blade rotates with angular velocity given by ω_z(t) = g - bt^2, where g = 5.00 rad/s and b = 0.800 rad/s^3. (b) Calculate the instantaneous angular acceleration α_z at t = 3.00 s and the average angular acceleration α_av-z for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why?
- Open QuestionCALC A fan blade rotates with angular velocity given by ω_z(t) = g - bt^2, where g = 5.00 rad/s and b = 0.800 rad/s^3. (a) Calculate the angular acceleration as a function of time.
- Open QuestionCP CALC The angular velocity of a flywheel obeys the equation ω_z(t) = A + Bt2, where t is in seconds and A and B are constants having numerical values 2.75 (for A) and 1.50 (for B). (b) What is the angular acceleration of the wheel at (i) t = 0 and (ii) t = 5.00 s?
- Open QuestionCALC The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct^3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = p/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s^2. (c) What are θ and the angular velocity when the angular acceleration is 3.50 rad/s^2?
- Open QuestionCALC The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct^3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = p/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s^2. (b) What is the angular acceleration when θ = p/4 rad?
- Open QuestionCALC The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct^3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = p/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s^2. (a) Find a, b, and c, including their units.
- Open QuestionA car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. (c) What is the speed of a point at the bottom edge of the tire?
- Open QuestionA car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. (b) What is the speed of a point at the top edge of the tire?
- Open Question
(II) The angular acceleration of a wheel, as a function of time, is α = 4.2 t² ― 9.0 t , where α is in rad/s² and t in seconds. If the wheel starts from rest (θ = 0 , ω = 0, at t = 0), determine a formula for
(b) the angular position θ, both as a function of time.
- Open Question
(II) Suppose the force Fₜ in the cord hanging from the pulley of Example 10–10, Fig. 10–22, is given by the relation Fₜ = 3.00 t ― 0.20 t² (newtons) where t is in seconds. If the pulley starts from rest, what is the linear speed of a point on its rim 9.0 s later? Ignore friction and use the moment of inertia, calculated in Example 10–10.