Question

A constant torque is applied to a rigid body whose moment of inertia is 4.0kg-m² around the axis of rotation. If the wheel starts from rest and attains an angular velocity of 20.0 rad/s in 10.0 s, what is the applied torque?

a) 2.0 N·m
b) 4.0 N·m
c) 6.0 N·m
d) 8.0 N·m

Answer 1

To calculate the torque applied to a rigid body with a given moment of inertia that reaches a specific angular velocity from rest, use the formula τ = Iα. The torque is found to be 8.0 N·m, which is option d).

Step-by-step explanation:

The question relates to the concept of rotational dynamics in Physics, and it involves calculating the torque when a constant force is applied to a rigid body with a known moment of inertia.

Using the formula τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration, we can find the torque. Given that the moment of inertia (I) is 4.0 kg-m² and the angular velocity (ω) reaches 20.0 rad/s from rest in 10.0 s, we first calculate the angular acceleration (α) using α = ω/t, where t is the time. Substituting the given values, the angular acceleration is α = 20.0 rad/s / 10.0 s = 2.0 rad/s².

Applying this to the formula τ = Iα, we get τ = (4.0 kg-m²)(2.0 rad/s²) = 8.0 N·m. Therefore, the applied torque is 8.0 N·m, which corresponds to option d).