1. A force F applied to a cord wrapped around a cylinder pulley. The ροπή is 2 N m and the στιγμή αδράνειας is 1 kg m2, τι είναι το γωνιώδης επιτάχυνση of the cylinder.
Γνωστό:
Ροπή (τ) = 2 N m
The moment of inertia (I) = 1 κιλά m2
Καταζητούμενος: The angular acceleration of the cylinder
Λύση:
Σε = Ι α
Σε = net torque, I = moment of inertia, α = angular acceleration
Angular acceleration of cylinder :
α = Στ / I = 2 / 1 = 2 rad/s2
2. A force F applied to a cord wrapped around a cylinder pulley. The magnitude of the force is 10 N, the radius of the cylinder is 0.2 m and the moment of inertia is 1 kg m2, What is the angular acceleration of the cylinder?
Γνωστό:
Δύναμη (F) = 10 N
Radius of cylinder (R) = 0.2 m
The moment of inertia (I) = 1 κιλά m2
Καταζητούμενος: The angular acceleration of the cylinder.
Λύση:
τ = F R
τ = torque, F = force, R = radius of cylinder
Ροπή:
τ = F R = (10 N)(0.2 m) = 2 N m
Σε = Ι α
Σε = net torque, I = moment of inertia, α = angular acceleration
Angular acceleration of cylinder :
α = Στ / I = 2 / 1 = 2 ακτίνια/δευτερόλεπτο2
3. A force F applied to a cord wrapped around a cylinder pulley. The magnitude of force is 10 N, the radius of cylinder is 0.2 m and the mass of cylinder is 20 kg m2,, What is the angular acceleration of the cylinder.
Γνωστό:
Δύναμη (F) = 10 N
Radius of cylinder (R) = 0.2 m
Mass of cylinder (M) = 20 kg
Ζητούνται: Angular acceleration of cylinder
Λύση:
τ = F R = (10 N)(0.2 m) = 2 N m
Ροπή αδράνειας:
I = 1⁄2 M R2 = 1⁄2 (20)(0.2)2 = 1⁄2 (20)(0.04) = 0.4 kg m2
Angular acceleration of cylinder :
α = Στ / I = 2 / 0.4 = 5 rad / s2
4. A 1-kg block hanging from a cord wrapped around a cylinder pulley. The moment of inertia of pulley is 1 kg m2 and the radius of pulley is 0.2 m. What is the angular acceleration of the pulley. Επιτάχυνση λόγω βαρύτητας είναι 10 m/s2.
Γνωστό:
Moment of inertia of pulley (I) = 1 kg m2
Μάζα of block (m) = 1 kg
Επιτάχυνση λόγω βαρύτητας (g) = 10 m/s2
Βάρος (w) = mg = (1 kg)(10 m/s2) = 10 kg m/s2 = 10 Β
Radius of pulley (R) = 0.2 m
Ζητούνται: Γωνιώδης επιτάχυνση
Λύση:
Ροπή:
τ = F R = w R = (10 N)(0.2 m) = 2 N m
Ροπή αδράνειας:
I = 1 kg m2
Angular acceleration :
α = Στ / I = 2 / 1 = 2 rad / s2
5. A 1-kg block hanging from a cord wrapped around a cylinder pulley. The mass of pulley is 20 kg and the radius of pulley is 0,2 m. What is the angular acceleration of the pulley and the ελεύθερη πτώση acceleration of the block. Acceleration due to gravity is 10 m/s2.
Γνωστό:
Mass of pulley (M) = 20 kg
Radius of pulley (R) = 0,2 m
Μάζα μπλοκ (m) = 1 kg
Επιτάχυνση λόγω βαρύτητας (g) = 10 m/s2
Βάρος (w) = mg = (1 kg) (10 m/s2) = 10 kg m/s2 = 10 Β
Ζητούνται: the angular acceleration of the pulley and the free fall acceleration of the block.
Λύση:
The torque :
τ = F R = w R = (10 N)(0.2 m) = 2 N m
Η ροπή αδράνειας της τροχαλίας του κυλίνδρου:
I = 1⁄2 M R2 = 1⁄2 (20)(0.2)2 = (10)(0.04) = 0.4 kg m2
The angular acceleration of the pulley :
α = Στ / I = 2 / 0.4 = 5 rad / s2
The free fall acceleration of the block :
a = R α = (0.2)(5) = 1 m/s2
