A uniform disk with mass 38.6 and radius 0.270 is pivoted at its center about a

Question

A uniform disk with mass 38.6 and radius 0.270 is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 29.0 is applied tangent to the rim of the disk. a)What is the magnitude of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.100 revolution? b)What is the magnitude of the resultant acceleration of a point on the rim of the disk after the disk has turned through 0.100 revolution?

Explanation / Answer

To convert from angular motion to linear motion multiply by the length of the radius. v = r * ?, a = r * a Linear distance = r * ? The force produces a torque, which causes the disc to accelerate. There are 2 equations for torque. Torque = I * a For a uniform disk, I = ½ * mass * radius^2 = ½ * 37 * 0.26^2 =1.2506 Torque = 1.2506 * a and Torque = Force * radius = 29 * 0.26 = 7.54 Set these 2 equations for torque equal to each other. 1.2506 * a = 7.54 a = 7.54 ÷ 1.2506 To determine the tangential velocity, you need to determine the tangential acceleration. Tangential acceleration = r * a = 0.26 * 7.54 ÷ 1.2506 Tangential acceleration is the same as the linear acceleration of a point on the rim of the disk. Since the force is constant, the acceleration is constant. The answer above is the answer to question b! Tangential velocity is the same as the linear velocity of a point on the rim of the disk. a.)What is the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.400 revolution? As the disk rotates one revolution, a point on the rim moves a distance which is equal to the circumference of the circle. Circumference = 2 * p * 0.26 = 0.52 * p 0.400 revolution = 0.4 * 0.52 * p = 0.208 * p meter This is the distance that the point moves. Since you do not know the time for the point to move this distance, use the following equation to determine the final velocity of the point. vf^2 = vi^2 + 2 * a * d vi = 0 m/s, a = 0.26 * 7.54 ÷ 1.2506, d = 0.208 * p

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