Physics Ch.10

Find the maximum range of the football in m, neglecting air resistance.

F=m(v^2/r)

What is the angular speed ωf of the system immediately after the collision, in radians per second?

L/I(f)

Calculate the moment of inertia of the merry-go-round, in kg ⋅ m2.

MR^2/2

What is the total moment of inertia If with respect to the hinge, of the rod-ball-system after the collision, in terms of the variables from the problem statement?

(ML^3/3)+mD^2

Immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry-go-round and boy.

(mR^2)w/I+mR^2

Surprisingly, the gum seems to remain stuck to the fan at this speed. Calculate the angular acceleration of the gum α, in radians per square second, as the fan is speeding up.

(wf-wi)/t

What is the initial angular momentum of the ball, in kilogram meters squared per second, right before the collision relative to the pivot point of the rod?

m(vcostheta)D

Calculate the kinetic energy Kw, in J, of the water wheel as it rotates.

mr^2

If the fan spins through 7.5 rotations during the spin up, calculate the work W in joules, that the fan's motor does on the fan.

ptheta

The shoe is in contact with the initially nearly stationary 0.500 kg football for 20.0 ms. What average force is exerted on the football in Newtons to give it a velocity of 22 m/s?

r=vt

Calculate the tangential component of the acceleration of the gum atan, in meters per square second, as the fan is speeding up.

ra

What is the magnitude of the centripetal acceleration of the gum arad, in meters per square second, when the fan reaches full speed?

rw^2

Calculate the magnitude of the linear velocity V, in meters per second, of the yo-yo after it has fallen a distance 0.36 m.

sqrt(2(g/3)H)

After passing point 2 the hill becomes frictionless and the ring's rotational velocity remains constant. What is the linear velocity of the ring at point 3 in m/s?

sqrt(2gh-r^2w^2)

Given h2 = 8 m, what is the velocity of the ring at point 2 in m/s?

sqrt(g(h1-h2))

How long does it take to come to rest in seconds?

t=-w(0)/a

Immediately before the boy jumps on the merry go round, calculate his angular speed (in radians/second) about the central axis of the merry-go-round.

v/r

What is the ring's rotational velocity in rad/s?

v2/r

How many revolutions does it make before stopping?

w(0)t+1/2at^2

If the velocity of the tip of the kicker's shoe is 36.5 m/s and the hip joint is 0.85 m from the tip of the shoe, what is the shoe tip's angular velocity in rad/s?

w=v/r

Assume that every second, 20% of the kinetic energy of the water wheel is transmitted to the grain mill. Calculate the power Pw in W of the grain mill based on the energy it receives from the water wheel.

1/2IW^2

Calculate the moment of inertia of the carousel about its axis, in units of kilogram meters squared.

1/2m(p)r(p)^2+8m(h)r(h)^2+4m(e)r(e)^2

Calculate the carousel's angular speed, in radians per second.

2pi/t

Calculate the angular velocity ωw of the water wheel in radians/sec.

2pif

Calculate the maximum the angular velocity of the fan ωmax, in radians per second.

2pif