A uniform horizontal disk of radius 5.50 m turns without friction at = 2.30 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 465 s. The sliding block experiences no friction. Its motion is constrained to have constant radial speed by a brake at B, producing tension in a light string tied to the block. (a) Find the torque as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by T 2mrvw. = t N.m (b) Find the value of this torque at t = 465 s, just before the sliding block finishes its motion. 2.52 N-m (c) Find the power which the drive motor must deliver as a function of time. t W/s (d) Find the value of the power when the sliding block is just reaching the end of the slot. 18.2 x w (e) Find the string tension as a function of time. ]t N/s

A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 2.36 m and a rotational inertia of 218 kg-m2 about the axis of rotation. A 72.6 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 2.07 rad/s when the student starts at the rim, what is the angular speed when she is 0.433 m from the center? Number i Units

A turntable 46.0 cm in diameter diameter starts from rest, and rotates at 68.0 rpm at its first complete revolution with constant angular acceleration. If it maintains the same acceleration, a) what is the rotational speed at time 34.0 seconds? b) what is the tangential speed of a point 10 cm from the edge of the turntable at time 34.0 seconds?

A wheel rotating with a constant angular acceleration turns through 15 revolutions during a 2 s time interval. Its angular velocity at the end of this interval is 18 rad/s. What is the angular acceleration of the wheel? Note that the initial angular velocity is not zero. Your answer

Your grandmother enjoys creating pottery as a hobby. She uses a potter's wheel, which is a stone disk of radius R = 0.540 m and mass M = 100 kg. In operation, the wheel rotates at 45.0 rev/min. While the wheel is spinning, your grandmother works clay at the center of the wheel with her hands into a pot-shaped object with circular symmetry. When the correct shape is reached, she wants to stop the wheel in as short a time interval as possible, so that the shape of the pot is not further distorted by the rotation. She pushes continuously with a wet rag as hard as she can radially inward on the edge of the wheel and the wheel stops in 6.00 s.   You would like to build a brake to stop the wheel in a shorter time interval, but you must determine the coefficient of friction (?k) between the rag and the wheel in order to design a better system. You determine that the maximum pressing force your grandmother can sustain for 6.00 s is 65.0 N. What If? If your grandmother instead chooses to press…

At t= 0 a grinding wheel has an angular velocity of 30.0 rad/s. It has a constant angular acceleration of 35.0 rad/s² until a circuit breaker trips at time t = 1.70 s. From then on, it turns through an angle 438 rad as it coasts to a stop at constant angular acceleration. Through what total angle did the wheel turn between t= 0 and the time it stopped? Express your answer in radians. 8= Submit Part B - ΑΣΦΑ 1 V Part C Request Answer At what time did it stop? Express your answer in seconds. Submit ΓΨΓ ΑΣΦ 3 Request Answer 2 @ 3 C www. 7 ΑΣΦ) → O ? What was its acceleration as it slowed down? Express your answer in radians per second squared. ? ? rad S Review Const

In a popular amusement park ride, a rotating cylinder of radius  R = 2.00 m  is set in rotation at an angular speed of 6.10 rad/s, as in the figure shown below. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider's clothing and the wall is needed to keep the rider from slipping?

Starting from rest, a wheel undergoes a constant acceleration for 10 seconds. When t = 3.0 s, the angular velocity of the wheel is 6.0 rad/s. Find the total angle the wheel rotates from t = 0 to t = 20 s.

A student gives a steady push to a ball at the end of a massless, rigid rod for 1 s, causing the ball to rotate clockwise in a horizontal circle as shown below. The rod’s pivot is frictionless. Sketch a graph of the ball’s angular velocity as a function of time for the first 3 s of the ball’s motion. You won’t be able to include numbers on the vertical axis, but your graph should have the correct sign and the correct shape

A Texas cockroach walks from the center of a circular disk (that rotates like a merry-go-round without external torques) out to the edge at radius R. The angular speed of the cockroach–disk system for the walk is (va = 5.0 rad/s and vb = 6.0 rad/s). After reaching R, what fraction of the rotational inertia of the disk does the cockroach have?