Question

A wheel of radius 20 cm and moment of inertia 1 kgm
can rotate about its centre. A string is wrapped over its rim and is pulled by a force
tangential to the rim of wheel. If angular acceleration produced is 2 rad/s
then the value of force
F
is​

Answer 1

Given:

A wheel of radius 20 cm and moment of inertia 1 kg m² can rotate about its centre. A string is wrapped over its rim and is pulled by a force tangential to the rim of wheel.

To find:

Value of force ?

Calculation:

Torque on the wheel can be represented as:

• I is moment of inertia.
• $\alpha$ is angular acceleration.
• $\tau$ is torque.

$\rm\therefore \: \tau = I \times \alpha$

$\rm \: \implies \: F \times r= I \times \alpha$

$\rm \: \implies \: F \times \dfrac{20}{100} = 1 \times 2$

$\rm \: \implies \: F \times 0.2 = 1 \times 2$

$\rm \: \implies \: F = 10 \: N$

So, force on the wheel is 10 N.