At what rate will a pendulum clock run on the Moon, where the acceleration due to gravity is 1.63m/s21.63m/s2, if it keeps time accurately on Earth? That is, find the time (in hours) it takes the clock’s hour hand to make one revolution on the Moon.

Case 1: A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takes t1 = 11.6 seconds to get up to its full speed of f1 = 78 revolutions per minute. Case 2: The DJ then changes the speed of the turntable from f1 = 78 to f2 = 120 revolutions per minute. She notices that the turntable rotates exactly n2= 12 times while accelerating uniformly.  t1 = 11.6 secondsn2 = 12 times  a. Calculate the angular speed described in Case 1, given as f1 = 78 revolutions per minute, into units of radians/second. b. How many revolutions does the turntable make while accelerating in Case 1?  c. Calculate the magnitude of the angular acceleration of the turntable in Case 1, in radians/second2.  d. Calculate the magnitude of the angular acceleration of the turntable (in radians/second2) while increasing to 120 RPM (Case 2).  e. How long (in seconds) does it take for the turntable to go from f1 = 78 to f2 = 120 RPM?

11.7 The motion of a particle is defined by the relation x = - 6- 36t – 40, where x and t are expressed in feet and seconds, respec- tively. Determine (a) when the velocity is zero, (b) the velocity, the acceleration, and the total distance traveled when x = 0. 11.8 The motion of a particle is defined by the relation x = - 9 + 24t - 8, where r and t are expressed in inches and seconds, respectively. Determine (a) when the velocity is zero, (b) the posi- tion and the total distance traveled when the acceleration is zero. 11.9 The acceleration of a particle is defined by the relation a = -8 m/s. Knowing that x = 20 m when t = 4 s and that r = 4 m when v = 16 m/s, determine (a) the time when the velocity is zero, (b) the velocity and the total distance traveled when t = il s.

A particle starts from the origin at t = 0 with a velocity of (16 - 12) m/s and moves in the xy plane with a constant acceleration of  = (3.0 - 6.0) m/s2. What is the speed of the particle at t = 2s?