A uniform-density wheel of mass 9 kg and radius 0.40 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 13 N for 0.72 s. (a) What is the final angular speed? Entry field with correct answer 5.2 radians/s (b) What was the average angular speed? Entry field with incorrect answer 1.872 radians/s (c) Through how big an angle did the wheel turn? Entry field with incorrect answer 1.3478 radians/s (d) How much string came off the wheel? Entry field with incorrect answer 0.8469 m

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒