A moment M is applied to uniform disc I of mass 20 kg and radius 0.2 m which drives another uniform disc II of mass 40 kg and radius 0.3 m, without slip occuring between them. If the angular acceleration of disc I is 8.33 rad/s² the value of M is Nm

To find the moment M applied to the first disc (disc I), we need to consider the relationship between torque, moment of inertia, and angular acceleration. The torque (τ) applied to an object is related to its moment of inertia (I) and angular acceleration (α) through the equation:

Understanding the Concepts

The formula we will use is:

τ = I * α

Where:

• τ is the torque applied (in Nm)
• I is the moment of inertia (in kg·m²)
• α is the angular acceleration (in rad/s²)

Calculating the Moment of Inertia for Disc I

For a uniform disc, the moment of inertia is given by the formula:

I = (1/2) * m * r²

For disc I:

• Mass (m) = 20 kg
• Radius (r) = 0.2 m

Plugging in the values:

I_I = (1/2) * 20 kg * (0.2 m)²

I_I = (1/2) * 20 * 0.04 = 0.4 kg·m²

Calculating the Torque for Disc I

Now that we have the moment of inertia for disc I, we can calculate the torque using the angular acceleration provided:

α = 8.33 rad/s²

Using the torque formula:

τ_I = I_I * α

τ_I = 0.4 kg·m² * 8.33 rad/s²

τ_I = 3.332 Nm

Relating Torque to Moment M

Since the discs are connected without slipping, the torque applied to disc I is equal to the moment M. Therefore, we find:

M = τ_I = 3.332 Nm

Final Result

The value of the moment M applied to disc I is approximately 3.33 Nm. This calculation illustrates how torque, moment of inertia, and angular acceleration are interrelated in rotational dynamics.