Classical Mechanics
# Torque

A fixed pulley-like device is used to lift a box of mass \(m=13\text{ kg},\) as shown in figure above. The outer radius of the device is \( R=7 \text{ m}, \) and the radius of the hub is \(r= 2 \text{ m}. \) When a constant horizontal force \( F = 130 \text{ N} \) is applied to a rope wrapped around the outer rim of the device, the box hanging from a rope wrapped around the hub acquires an upward acceleration of magnitude \( 2 \text{ m/s}^2. \) Then what is the rotational inertia of the device about its axis of rotation?

The gravitational acceleration is \( g= 10 \text{ m/s}^2. \)

A cubic dice is sliding on a frictionless table. The dice is a cube with edges of length 1 cm and a mass of 30 g. A kid reaches down and gives a horizontal flick to the dice, causing it to change which face is up. What is the minimum impulse in **g~cm/s** the kid must give to the dice in order to change the face?

**Details and assumptions**

- The acceleration of gravity is \(-9.8~m/s^2\).
- You can model the dice as a perfect cube of uniform density.
- The dice never leave the table

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