1) A sphere of radius r =34.5 cm and massm = 1.80 kg starts from rest and rolls

Question

1) A sphere of radius r =34.5 cm and massm = 1.80 kg starts from rest and rolls without slipping down a 30.0 incline that is 10.0 m long.

C) What is the ratio of translational to rotational kinetic energy at the bottom?

Express your answer using three significant figures.

D) Avoid putting in numbers until the end so you can answer: do your answers in previous parts depend on the radius of the sphere or its mass?

2) Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration.

A) What is the magnitude of the angular acceleration of the salad spinner as it slows down?

Express your answer numerically in radians per second per second.

Explanation / Answer

r =34.5 cm , m =1.8 kg, theta =30 degrees, l =10cm

h = l*sin(30) = 10*sin(30) =5 cm

(c) tanslational kinetic energy Kt = (1/2) mv2

For sphere Moment of inertia I =(2/5)mr2

Rotational kinetic energy Kr =(1/2)Iw2 = (2/10)mv2

where v =rw

Kt/Kr = [ (1/2) mv2 ]/[ (2/10) mv2 ] =2.5

(d) No

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