A large stone disk is viewed from above and is initially at rest as seen in the

Question

A large stone disk is viewed from above and is initially at rest as seen in the figure below. The disk has a mass of 220.0 kg and a radius of 2.500 m. A constant force of40.0 N is applied tangent to the edge of the disk for 64.0 s, causing the disk to spin around the z axis.

(a) Calculate the angular acceleration of the stone, finding both the direction and magnitude. (Express your answer in vector form. Substitute numeric values, do not use variables.)

(b) What is the final angular velocity of the stone? (Express your answer in vector form. Substitute numeric values, do not use variables.)

(c) Calculate the translational speed for a point on the edge of the stone after 64.0 s.
____ m/s

Explanation / Answer

PArt A : use the formula for torque acting on stone T = r x F = IA

where A is angular accleration

so

T = r i x Fj = 0.5 mR^2 A

A = 2F/MR

A = 2* 40/(220 * 2.5)

A = 0.145 rad/s^2

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part B :

use Wt = Wo + A t

W = 0 + 0.145 * 64

W = 9.28 rad/s

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part C:

use V = r W

so

V = 2.5 * 9.28

V = 23.2 m/s

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