Could you please help me figure out the formulas to solve the following? Thank y

Question

Could you please help me figure out the formulas to solve the following? Thank you! r2= 6 cm 9. Forces are applied by ropes as shown above to a cyinder of unitorrtia o density with a mass of 5 kg and a radius r-6 cm. (Assume the inertia of the attached pulle What is the net torque applied? a. 0.224 m-N b. 1.6 m N c. 0.096 m-N d. 0.32 m-N y with radius r, is negligible). . What will be the sense of rotation? a. counterclockwise b. clockwise What is the moment of inertia of the cylinder? (assume the cylinder has uniform density and radius equal to r a, 6.3 x 10-3 kg b. 0.0108 kg-m c. 0.0216 tm d. 9 x 10 3 kg-m

Explanation / Answer

(39):

Torque vector = (radious vector)* Force

here angle between F1 and R1 is 90 degree and that between F2 and R2 is also 90 degree

take anticlockwise rotation as +ve and clockwise rotation as negative

net torque = 6*(6/100)*sin(90) - 1*(4/100)*sin(90)

net torque = 0.32 Nm

(40):

sense of rotation will be counterclockwisebecause the net torque is in counter clockwise direction.

(41):

I = Mr^2 = 5*(6/100)^2 = 0.0180 kgm^2

(42):ot

moment of inertia of cyliner with inner radius r1 and outer radius r2 is

I = 1/2 * M * (R1^2 + R2^2) = 1/2* 5 * ( (6/100)^2 + (4/100)^2 ) = 0.0130 kg m^2

therefore angular acceleration = torque / I = 0.32 / 0.0130 = 24.6 rad/s

(43):

angular vel after 62 sec. = omega final

omega final = omega initial + angulat acc. * time

omega final = 0 + 24.6*62 = 1.525*10^3 rad/s

(44):

angular displacement = omega initial * t + (1/2)*angular acc.* t^2

angular displacement = 2.709810^6 degree

(45):

yes friction does require for perfect rolling else ball will slip and rotate at it's own place without moving.

(46):

a ball can't roll on a frictionless surface because even if tries to do so it will slip and will kepp on rotating at its own place.

(47):

no the ball will not roll on an inclined frictionleess surface because it will slide on inclined plane and will rotate as well but there won't be any synchronization between sliding (moving on inclind plane) and rotation of ball , hence we can't call it rolling.

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