Problem 5) (Conservation of angular momentum) A merry-go-round with a radius of 2.5 meters and mass of M = 175 kg has an angular velocity of 0.5 rev/s. A boy with a mass of m = 25 kg runs and jumps tangentially on the edge of the merry- go-round and holds on the rail. What is the final angular speed of the boy+merry-go-round? (Hint: the initial angular momentum of the kid is mass times velocity times the radius, i.e., mvr, and his final moment of inertia is mr²).

QUESTION 7 What is the total kinetic energy of a bowling ball of mass, m, and radius, R, that is rolling in a straight line with a center-of-mass velocity, vcm: without slipping on a level bowling lane? Assume that the bowling ball is a uniform, solid sphere. (Neglect rolling friction.) a. 7m| v ст 10 ("m)² b. m V ст 2 c. Sm(v cm)² ст 3m v ст 4 е. 2m v ст 3 2. 6

A sanding disk with a rotational inertia of 1.2 x 10-3kgm2 is attached to an electric drill whose motor delivers a torque of 16 Nm.  If the torque is applied for 25 ms and the disk starts from rest, what is the magnitude of the angular velocity of the sanding disk?  Use the rotational version of the Impulse Momentum Theorem.  Take note of the time units.

An isolated system consists of a single object, which initially moves without friction at velocity ux along a horizontal x-axis. After an internal explosion, the object splits into two parts, A and B. The figure shows the masses and speeds of these parts immediately after the explosion. None of these objects rotates. 1.50 m s-¹ 2.00 kg A Final kinetic energy initial kinetic energy 3.50 m s-¹ - 3.00 kg What is the difference between the total final kinetic energy of A and B and the initial kinetic energy of whole object? Give you answer by entering a number, specified to an appropriate number of significant figures, into the empty box. B J.

A gymnast with a mass of 55 kg flipped in the air and achieved a maximum angular velocity of 445 degrees/sec just before landing from the flip. a) What is the magnitude of the angular impulse in kg*m2/s exerted by the floor on the gymnast when they stuck the landing and came to a complete stop, if they had a radius of gyration of 0.75 meters throughout the landing and their initial angular velocity just as they hit the floor was equal to the maximum angular velocity of 445 degrees/sec?

Ballistic pendulum: A projectile of mass m = 1 kg is fired with an initial speed v0 = 20 m/s at the bob of a pendulum with radius R = 3 m. The bob has mass M = 4 kg and is suspended by a rod of negligible mass. After the collision the projectile and bob stick together and swing at speed vf through an arc reaching height h and stop. (assume g=10 m/s2) (1) What is the speed vf just after the collision ?  (2) What is the total kinetic energy for projectile and bob together just after the collision?

A light rigid rod of mass 3.00 kg and length 2.00 m rotates about an axis perpendicular to its length and passing through its center as shown in the figure below. Two particles of masses m1 = 6.00 kg and m2 = 3.50 kg are connected to the ends of the rod. What is the angular momentum of the system if the speed of each particle is 4.05 m/s? m2

The position vector of a particle of mass 1.0 kg as a function of time is given by F= (6f + 10 tj ) m where 7 is in meters and t is in seconds. Determine the angular momentum of the particle about the origin as a function of time (in kg m2/s)? Option 1 Option 2 Option 3 Option 4 Option 5 (20 tj) (120 tj) (60 tj) (30 tj) (240 tj)

Candace is a 53 kg diver. At the instant of takeoff, her angular momentum about her transverse axis is 20 kg.m7s. Her radius of gyration about the transverse axis is 0.4 m at this instant. During the dive, Candace tucks and reduces her radius of gyration about thetransverse axis to 0.18 m.a) At takeoff, what is Candace's moment of inertia about her transverse axis? kg*m?b) At takeoff, what is Candace's angular velocity in degrees/sec about the transverse axis?c) After Candace tucks, what is her moment of inertia about her transverse axis? kg*m? d) After Candace tucks, what is her angular velocity in degrees/sec about the transverse axis?

62