simple yo-yo consists of a hoop of radius R with a string wound around the rim several times. The free end of the string is held fixed, and the hoop released from rest. The string unwinds without slipping. a) Use forces and torques to find the hoop’s acceleration. b) Use this acceleration and kinematics to find the hoop’s linear speed after it has descended a distance D. Compare with your result from HW#20,

A solid metal disk with moment of inertia I, radius R, and mass m1 can rotate freely about a frictionless axis passing through its center. A light string is wrapped around the disk and connects to a hanging mass m2. The hanging mass is released from rest at a distance d above the ground and accelerates downward with acceleration awhile the disk rotates through an angle q. a)  Draw free body diagrams for the disk and the hanging mass. b) Find an expression for the angular accelerationaof the diskin terms of m2, I, R, and any necessary constants. c) Find an expression for the time it takes for the hanging mass to reach the ground. Write your answer in terms of q, a, and any necessary constants.

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LAA-2 A solid disk of radius 15.0cm starts at rest and reaches a final angular speed of 1,200rev/min clockwise after turning thru a total of 80.0 revolutions. rotation a) Find the (constant) angular acceleration of the disk in units of radians and seconds. b) Find the final linear speed in m/s of point P on the rim of the disk. c) Find the magnitude of the tangential acceleration of point P on the rim of the disk. point P R=15.0cm d) Find the magnitude of the radial acceleration of point P on the rim of the disk. e) Sketch on your paper a figure like the one to the right and show arrows that represents atan and arad at point P. 9:47 PM 梦 0 arch 66°F Mostly cloudy 9/23/2021 Gup ISTRUCTION

An old vinyl record is played on a turntable that turns at a rate of 45 rotations per minute. Find the angular speed in radians per second. Give your answer as a fraction and do not include units. Keep your answer in terms of π if necessary.

Consider the 15.0 kg motorcycle wheel shown in the figure. Assume it to be approximately an annular ring with an inner radius of R1 = 0.280 m and an outer radius of R2 = 0.480 m. The motorcycle is on its center stand, so that the wheel can spin freely. a)If the drive chain exerts a force of 2450 N at a radius of 5.00 cm, what is the angular acceleration of the wheel in rad/s2? _____rad/s2   (b)What is the tangential acceleration, in m/s2, of a point on the outer edge of the tire? ______m/s2   (c)How long in seconds, starting from rest, does it take to reach an angular velocity of 80.0 rad/s? _______s