HW 6- Rotation

A civil engineer is asked to design a curved section of roadway...What is the minimum radius of curvature of the curve?

r = v^2 (1 - μs^2)/2 μsg *convert km/hr to m/s

A particle on a string is whirled in a circle at constant speed...Choose the diagram showing the components of the acceleration vector at that instant.

single arrow pointing to the left ("towards middle"

A dentist's drill starts from rest. After _____ s of constant angular acceleration it turns at a rate of __________ rev/min....... Throughout what angle does the drill rotate during this period?

θ = wot + 1/2 αt^2

An air pick of mass __ kg is tied to a string and allowed to revolve in a circle of ___ m on a frictionless horizontal surface...What is the magnitude of the force that maintains circular motion acting on the puck?

F = mg (mass of tied rope x gravity) *m = mass tied to it

The planet Krypton has a mass of _____ kg and radius of _______. What is the acceleration of an object in free fall near the surface of Krypton?

Fg = Gm/r^2

Consider a conical pendulum... What is the correct free body diagram showing only the forces acting on the mass?

2 forces total; Tension pointing towards left string and mg down

A disk with a radius of 0.1 m is spinning about its center with a constant angular speed of 10 rad/sec. What are the speed abc magnitude of the acceleration of a bug clinging to the rim of the disk?

A: 1 m/s and 10 m/s^2 Equations: Speed; v = rw Acceleration; a = w^2r

A civil engineer is asked to design a curved section of roadway...At what angle should the road be banked?

Equation: Tan-1 (μ) **make sure answer is in degrees!

A coin is placed __ cm from the center of a horizontal turntable, initially at rest. The turntable then begins to rotate...What is the coefficient of static friction between the coin and the turntable?

Equation: Us (static friction) = v^2/r x g

A grinding wheel, initially at rest is rotated...Determine the time needed to bring the wheel to rest.

Equation: Vf = Vo + at *Vf is 0, Vo is velocity you solved for earlier

A hawk flies in a horizontal arc of radius ___ m at a constant speed of ___ m/s... It continues to fly along the same horizontal arc but increases its speed at the rate of 1.49 m/s^2. Find the MAGNITUDE of acceleration under new conditions.

Equation: a = sqrt a1^2 + a2^2

A hawk flies in a horizontal arc of radius ___ m at a constant speed of ___ m/s. Find its centripetal force.

Equation: a = v^2/r

A bucket full of water is rotated in a vertical circle of radius _____ m. What must be the minimum speed of the pail at the top of the circle if no water is to spill out?

Equation: v = sqrt (g x r)

An air pick of mass __ kg is tied to a string and allowed to revolve in a circle of ___ m on a frictionless horizontal surface...What is the linear speed of the puck?

F = m (v^2/r) * m is mass of puck * F is magnitude of force found in previous step

You launch two earth satellites into orbits at different radi. Is it possible for the satellite at lower altitude to stay directly below the state kite at higher altitude?

No; impossible

A rigid circular wheel spins at a constant angular velocity about a stationary axis. Choose the picture below that correctly describes the relative magnitudes and directions of the velocity vector of points on the wheel.

Picture with 4 total arrows inside wheel moving at constant and changing direction

A dentist's drill starts from rest. After _____ s of constant angular acceleration it turns at a rate of __________ rev/min. Find the drill's angular acceleration in units if rad/s^2.

Step 1: convert ________ rev/min to rad/sec Step 2: α = Δw/Δt; wf - wi/t

The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks....What is the speed of the bullet?

Step 1: convert rev/min to degrees/second (1 rev = 360 degrees) and convert distance (cm to m) Step 2: Solve for time using the equation, t = angle/speed Step 3: Solve for speed using speed = distance (m) over time

A grinding wheel, initially at rest is rotated...Find the angular acceleration required to bring the wheel to rest.

Step 1: find final velocity using the equation, w = wo + αt Step 2: concert deceleration from rev to rad (___ rev x 2 pi) to use as displacement (s) Step 3: Use the equation wf^2 = wo^2 + 2as to solve for angular acceleration

An earth satellite remains in orbit at a distance of _______ km from the center of the earth. What speed would it have to maintain?

V = sqrt GM/r *concert radius from km to m

A car rounds a curve while maintaining a constant speed. Is there a net force on the car as it rounds the curve?

Yes- its direction is changing

Let the turntable spin faster and faster with constant angular acceleration. Which sketch qualitatively shows the direction of the acceleration vector a of the bug?

a is inside the disk and points up to the left