Athin, cylindrical rod ℓ = 27.0 cm long with a mass m = 1.20 kg has a ball of diameter d = 10.00 cm and mass m = 2.00 kg attached to one end. the arrangement is originally vertical and stationary, with the ball at the top as shown in the figure below. the combination is free to pivot about the bottom end of the rod after being given a slight nudge.

(a) after the combination rotates through 90 degrees, what is its rotational kinetic energy?

(b) what is the angular speed of the rod and ball?

(c) what is the linear speed of the center of mass of the ball?

(d) how does it compare with the speed had the ball fallen freely through the same distance of 32.0 cm?

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 ⇒

What is a good example of instantaneous speed

The mass of a bowling ball is 10 kg and the mass of a ping pong ball is 0.015 kg. if the two objects are 5 meters apart, what is the gravitational force ?