When the resistance is offered by the body to continue to be in the uniform motion unless an external force acts on it. Or, in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis. The moment of inertia is also known as the angular mass or rotational inertia. An object of mass 100 kg is accelerated uniformly from a velocity of 5 ms–1 to 8 ms–1 in 6 s.
Access Answers of Science NCERT class 9 Chapter 9: Force and Laws Of Motion(All intext and exercise questions solved)
The radius of the ring is taken as R and its mass as M. All the elements are at the same distance from the axis of rotation, R. A hockey ball of mass 200 g travelling at 10 ms–1 is struck by a hockey stick so as to return it along its original path with a velocity at 5 ms–1. Calculate the magnitude of change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick. Since the velocity of the cabinet is constant, its acceleration must be zero.
Moment of Inertia of Rigid Bodies
A bullet of mass 10 g travelling horizontally with a velocity of 150 m s–1 strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet. An object moving in some direction with constant velocity will continue in its state of motion as long as there are no external unbalanced forces acting on it.
- From a uniform circular disc of radius R and mass 9 M, a small disc of radius R/3 is removed, as shown in the figure.
- The moment of inertia of a sphere expression is obtained in two ways.
- Usually, MOI is used to calculate angular momentum.
- (d) there is no unbalanced force on the ball, so the ball would want to come to rest.
- The moment of inertia (I) is mostly specified based on the distribution of mass in the body with respect to the axis of rotation.
- An object moving in some direction with constant velocity will continue in its state of motion as long as there are no external unbalanced forces acting on it.
- According to the third law of motion when we push on an object, the object pushes back on us with an equal and opposite force.
Calculation of Moment of Inertia
Also calculate the magnitude of the force required. As per the law of conservation of momentum, the total momentum before the collision between the insect and the car is equal to the total momentum after the collision. Therefore, the change in the momentum of the insect is much greater than the change in momentum of the car (since force is proportional to mass).
NCERT Solutions For Class 9 Science Chapter 9: Force and Laws Of Motion
- Since inertia is dependent on the mass of the object, the object with the greater mass will hold greater inertia.
- However, Rahul’s suggestion that the change in the momentum is the same contradicts the law of conservation of momentum.
- This causes the passengers to fall forwards when the brakes are applied.
- Let M and R be the mass, and the radius of the sphere, O at its centre and OY be the given axis.
- However, the inertia of the leaves in attached to the branch resists the motion of the branch.
- Inertia is the resistance offered by a body to the motion whereas momentum is the tendency of a body to continue moving.
A student justifies this by answering that the two opposite and equal forces cancel each other. Comment on this logic and explain why the truck does not move. Moment of inertia from a Physics point of view is basically a quantitative measure of the rotational inertia or the angular mass of a body. In simple terms, it is the opposition that the body exhibits to the change in rotation about an axis which may further be internal or external.
From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s–1. Calculate the initial recoil velocity of the rifle. Consider a wheel and a uniform disc, both having the same mass rotating about the same axis. As you may have observed, it is more difficult to start or stop the wheel than it is to start or stop the uniform disc. As the hollow sphere is uniform, %KEYWORD_VAR% the surface mass density (M/A) is constant. The width of this ring is Rdθ, and its periphery is 2πRsinθ.
However, the inertia of the leaves in attached to the branch resists the motion of the branch. Therefore, the leaves that are weakly attached to the branch fall off due to inertia whereas the leaves that are firmly attached to the branch remain attached. First, when a football player kicks a football to another player, second when that player kicks the football to the goalkeeper. Fourth, when the goalkeeper kicks the football towards his team player. Since inertia is dependent on the mass of the object, the object with the greater mass will hold greater inertia. The following objects hold greater inertia because of their mass.
Inertia is the resistance offered by a body to the motion whereas momentum is the tendency of a body to continue moving. Let us look at the differences between the two to understand the concept better. The moment of inertia of a rigid body depends only on the distribution of mass of the body about the axis of rotation and is independent of the speed of rotation. Hence, the moment of inertia of a rigid body does not change with the speed of rotation. The change in momentum of the insect and the motorcar is equal by conservation of momentum.
The mass is spread over the surface of the sphere, and the inside is hollow. Consider a uniform rod of mass M and length L, and the moment of inertia should be calculated about the bisector AB. As per the third law of motion, the nail exerts an equal and opposite force on the hammer. Since the force exerted on the nail by the hammer is N, the force exerted on the hammer by the nail will be +2500 N. (a) The distance covered by the object at any time interval is greater than any of the distances covered in previous time intervals. Therefore, the acceleration of the object is increasing.