The pulley shown in the illustration has a radius of 2.70 m and a moment of iner
ID: 1470346 • Letter: T
Question
The pulley shown in the illustration has a radius of 2.70 m and a moment of inertia of 39.0 kg·m2. The hanging mass is 4.20 kg and it exerts a force tangent to the edge of the pulley. What is the angular acceleration of the pulley?
A child pushes a merry-go-round with a force of 55.0 N at an angle tangent to the circle (that is, perpendicular to a radius). If the child pushes it through exactly one full circle, and the merry-go-round has a radius of 1.15 m, how much work does she do?
A solid uniform sphere of mass 3.1 kg and radius 0.052 m rotates with angular velocity 7.5 rad/s about an axis through its center. Find the sphere’s rotational kinetic energy.
A solid uniform cylinder of mass 4.3 kg and radius 0.054 m rolls without slipping at a speed of 0.72 m/s. What is the cylinder’s total kinetic energy?
An ice skater spins on the tip of her skate and gradually pulls in her arms and leg to reduce her moment of inertia by a factor of 2.0. Ignoring external torques, by what factor does the skater’s angular velocity increase?
You swing a 0.23-kg penguin statue around in a horizontal circle at the end of a 0.89-m long string. The statue’s speed is 6.3 m/s. What is the magnitude of its angular momentum?
The pulley shown in the illustration has a radius of 2.70 m and a moment of inertia of 39.0 kg·m2. The hanging mass is 4.20 kg and it exerts a force tangent to the edge of the pulley. What is the angular acceleration of the pulley?
A child pushes a merry-go-round with a force of 55.0 N at an angle tangent to the circle (that is, perpendicular to a radius). If the child pushes it through exactly one full circle, and the merry-go-round has a radius of 1.15 m, how much work does she do?
A solid uniform sphere of mass 3.1 kg and radius 0.052 m rotates with angular velocity 7.5 rad/s about an axis through its center. Find the sphere’s rotational kinetic energy.
A solid uniform cylinder of mass 4.3 kg and radius 0.054 m rolls without slipping at a speed of 0.72 m/s. What is the cylinder’s total kinetic energy?
An ice skater spins on the tip of her skate and gradually pulls in her arms and leg to reduce her moment of inertia by a factor of 2.0. Ignoring external torques, by what factor does the skater’s angular velocity increase?
You swing a 0.23-kg penguin statue around in a horizontal circle at the end of a 0.89-m long string. The statue’s speed is 6.3 m/s. What is the magnitude of its angular momentum?
What is the magnitude of angular momentum of a 1190 kg car going around a circular curve with a 15.0 m radius at 12.0 m/s? Assume the origin is at the center of the curve's arc.Explanation / Answer
1)
for hanging mass m*g - T = m*a
T = m*g - m*a
for pulley
T*R = I*alpha
(mg - ma)*R = I*a/R
mg - ma = I*a/R^2
a = mg/(m + I/R^2)
a = (4.2*9.8)/(4.2 + (39/2.7^2))
a = 4.31
alpha =a/R = 1.59 rad/s^2
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work = torque*angular displacement = R*F*theta = 1.15*55*2*pi = 397.4 J
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KE = 0.5*I*w^2 = 0.5*(2/5)*3.1*0.052^2*7.5^2 = 0.0943 J
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KE = KEt + KEr
KE = 0.5*m*v^2 + 0.5*I*w^2
KE = 0.5*m*v^2 + 0.5*0.5*m*R^2*v^2/R^2
KE = 0.75*m*v^2 = 0.75*3.1*0.72^2
KE = 1.21 J
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