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A compact motor pulley is utilized to spin a large grinding disc. The pulley and disc are aligned so their outer rims make contact. The motor pulley, with a radius of 8.0 cm, accelerates at 8.0 rad/s² and remains in touch with a grinding disc that has a radius of 22.0 cm without experiencing any slippage. Determine what the grinding disc's angular acceleration value will be.
A sphere follows a circular trajectory such that its angular position follows θ(t) = X + Yt - Zt3, where θ is measured in radians, t is measured in seconds, and X, Y, and Z are constants. At t = 0, the angular position of the X is θ = π/3 while the angular velocity is 1.30 rad/s. In another instance, t = 1.80 s, the sphere has an angular acceleration of 0.900 rad/s2. At the moment where angular accleration is 2.80 rad/s2, determine the values of angular velocity and angular position.
A wind turbine of diameter 1200 mm spins at an angular velocity ω = [8.0 - (1/4)t2] rad/s, where t is measured in seconds. Find the turbine's angular acceleration at t = 6.0 s.
A wheel has a decoration mounted 20 cm from the axis of the 700 mm wheel. An observer notices that the wheel makes 5 turns every second. Calculate the speed (in m/s) and net acceleration of the decoration.
When a motor is switched off, rotational inertia and kinetic energy keep some parts rotating. A shaft experiences a steady decrease in angular frequency changing from 650 rev/min at t = 0 s to 300 rev/min at t = 3.50 s. At what time (t = ? not Δt) does the shaft stop assuming the angular accleration remains the same until it stops?
The rotor of the centrifuge accelerates a sample tube at a constant rate. The tube is initially at rest. After 35 s of rotation, the tube's angular speed is 1600 rpm. Calculate the tube's angular acceleration.
The disk of a sander machine rotates at a constant speed of 700 rpm. The disk's diameter is 10 cm. Suddenly, the machine fuse blows, and the disk takes 36 s to stop. Calculate the linear velocity of a point on the disk's outer edge 15 s after the fuse blows.
A wind turbine has a steady angular acceleration of 0.100 rad/s2 and an initial angular speed of 0.50 rad/s. Find: i) its angular speed after 4.0 seconds, and ii) the angle the turbine will have turned through between t = 0 and t = 4.0 seconds.