Question

Obtain an expression for the torque acting on a rotating body with constant angular acceleration. Hence state the dimensions and SI unit of torque.

Obtain an expression for the torque acting on a rotating body with constant angular acceleration.

Obtain an expression relating the torque with angular acceleration for a rigid body.

Answer 1

For m₁, a₁ = r₁α

For m₂, a₂ = r₂α

For m_n, a_n = r_nα

f₁ = m₁a₁ = m₁r₁α

f₂ = m₂a₂ = m₂r₂α

f_n = m_nr_nα

Torque `(vec tau) = vec r xx vec f`

= r f sin 90°

τ = rf

τ₁ = rf₁ = `m_1 r_1^2alpha`

τ₂ = `m_2 r_2^2 alpha`

τ_n = `m_n r_n^2 alpha`

τ = τ₁ + τ₂ + ... + τ_n

Total torque on  the body,

`vec tau_"net" = vec tau_1 + vec tau_2 + vec tau_3 + ... vec tau_n`

= `m_1 r_1^2 alpha + m_2 r_2^2 alpha + ..... + m_n r_n^2 alpha`

= `alpha(m_1 r_1^2 + m_2 r_2^2 + ..... + m_n r_n^2)`

I = mr²

`vec tau_"net"` = (I₁ + I₂ + I₃ + ...... I_n)α

= Iα

Dimension: [ML²T⁻²]