Phys Quiz: Rotational Motion

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Phys Quiz: Rotational Motion

Answer each of the following.  Show your steps.  Write the equation you are using, fill in the known values, and then give the answer--including units.  Box your answer.

 

1. A merry-go-round is rotating at 12 RPM.  What is its angular velocity in rad/s?

ω = 12 (2π) /60 = 0.4π = 1.26

 


2. A merry-go round is rotating at 8.0 rad/s. If the merry-go-round is brought to a stop in 2 revolutions, what is its average angular acceleration during that time?

0 = 64 + 2 α (4π)       α =  – 2.55

2 (4π)                     − 8

Alternative approach:                                                                                                           8                                            Δt  .

 


3.  Three forces are applied to a compound pulley as shown tin the diagram.  The radii are 20, 40, and 60 cm respectively.  Given the following forces, what is the magnitude and direction of the net torque acting on the pulley?

Force A = 20 N

Force B = 40 N

Force C = 10 N

20(0.6) – 40(0.4) + 10(0.2) à


Force A


 

Force C


 

 

 

 

 

A) What is the inertia of the rod/mass system about C?

 

IC  = 12(1.62)/12  + 5(0.82) = 2.56 + 3.2 = 5.76

 

 

B) At the instant it’s released, what is the net torque acting on the rod/mass system about C?

 

 

τ = 5(9.8)(0.8) = 39.2

 

 

C) What is its initial angular acceleration?

 

α =  = = 6.81


 

 

 

 

 

 

 

C

 

 

 

7.  A disc and a hoop roll without slip up a ramp.  The two objects have the same mass, radius, and initial speed, v.

 

Which object will reach the greatest vertical height H?  Circle the best answer.

 

Disc                    Hoop                 Neither, both will reach same height.

 

Explain your answer with physics.  Think before you write.  Try to be direct and specific.  Use words and sentences, not equations.

Hoop.  The disc and the hoop have the same speed and radius—so they have   the same angular velocity. Kinetic energy is the sum of the translational and       rotational parts.  Since the two shapes have the same mass, they have the same translational KE. The rotational KE is proportional to the inertia of the shape      and the hoop has a larger inertia. Since the two have the same angular velocity and the hoop has more inertia, it has more rotational kinetic energy.  The hoop has more kinetic energy to change into gravitational PE—so the hoop goes       higher.



















2022-04-12