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Chapter 6: Problem 31

When the disc stops skidding and begins to roll without slipping, its speed will be (A) \(R \omega_{0}\) (B) \(\frac{1}{3} R \omega_{0}\) (C) \(\frac{1}{2} R \omega_{0}\) (D) \(\frac{1}{4} R \omega_{0}\)

Short Answer

Expert verified
The disc's speed when it starts rolling without slipping will be \(R \omega_0\) (Option A).

Step by step solution

01

Identify the quantities given and required

The given quantities are the initial angular velocity \(\omega_0\) and the radius \(R\) of the disc. The problem is asking for the speed of the disc once it starts rolling without slipping.
02

Understand the relation between linear velocity and angular velocity in rolling motion

In the rolling motion without slipping, the linear velocity \(v\) of the disc and its angular velocity \(\omega\) are related by the equation \(v = R \omega\). In this case, when the disc starts rolling without slipping, we replace \(\omega\) by \(\omega_0\).
03

Plug in the initial angular velocity \(\omega_0\) into the equation

We now have the equation \(v = R \omega_0\). This gives us the speed of the disc when it starts rolling without slipping.

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