An astronaut is being tested in a centrifuge. the centrifuge has a radius of 9 m and, in starting, rotates according to ? = 0.30t2, where t is in seconds and ? is in radians.

(a) when t = 9.0 s, what is the magnitude of the astronaut's angular velocity?

(b) when t = 9.0 s, what is the magnitude of the astronaut's linear speed?

(c) when t = 9.0 s, what is the magnitude of the astronaut's tangential acceleration?

(d) when t = 9.0 s, what is the magnitude of the astronaut's radial acceleration?

28. a stone is projected at a cliff of height h with an initial speed of 42.0 mls directed at angle θ0 = 60.0° above the horizontal. the stone strikes at a, 5.50 s after launching. find (a) the height h of the cliff, (b) the speed of the stone just before impact at a, and (c) the maximum height h reached above the grou

Asher cycles 12 miles in 16 hours. what is his speed?

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 ⇒