A solid puck with radius R_1 = 1 m and mass M = 1.5 kg is sitting on a friction

Question

A solid puck with radius R_1 = 1 m and mass M = 1.5 kg is sitting on a friction table. A top view of the puck is shown in the figure. Three constant forces are applied to in y = shown: F_1 = 3 N and F_2 = 5 N are applied at radius R_1, while F_3 = 4 N is applied at radius R_3 = 0.4 m. What is the angular acceleration of the puck? A) 0.5 rad/s^2 B) 1.9 rad/s^2 C) 2.1 rad/s^2 D) 2.8 rad/s^2 E) 6.0 rad/s^2 The puck begins to rotate in the A) Clockwise direction B) Counterclockwise direction C) Does not rotate

Explanation / Answer

Here,

let the angular acceleration is a

Using seocnd law of motion

moment of inertia * a = net torque

0.5 * 1.5 * 1^2 * a = 3 * 1 + 4 * 0.40 - sin(30) * 5 * 1

solving for a

a = 2.8 rad/s^2

the angular acceleration is 2.8 rad/s^2

part b)

the puck begins to rotate in the B) counter clockwise direction

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