 Solution

ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/section-b/6/b/solution

Let

I_{⊥}

denote the moment of inertia normal to the disc and

I_{d}

I_{⊥} = 2 I_{d}

. The intended angular impulse has magnitude

J = I_{⊥} ω_{0}

; delivering that magnitude about a diameter instead gives

J = I_{d} ω

. Thus

I_{d} ω = 2 I_{d} ω_{0}, ω = 2 ω_{0} .

These are principal axes, so angular momentum is parallel to angular velocity in both cases. Equal delivered angular impulse means equal magnitude of the change in angular momentum, not equal rotational kinetic energy; the actual rotational kinetic energy is twice the intended value.

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