Tangential force acting on a stationary body in space

Assume a motionless body with mass in space. And assuming a totally tangential force (θ=90° to the radius) acting on the surface area of the body (dA→0). Will the body react with totally rotational motion due to torque produced (τ=tangential force x radius) without any linear motion (as there's no force component in the direction to center of mass)?

Please refer diagram

#Mechanics

Note by Ahmad Faisal
3 years, 5 months ago

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Comments

Put a pen on a clean table. Try hitting it with a tangential force with your pointing finger. Observe its motion. Now in space there will be no friction or air resistance. What you have observed for the pen as such will go on forever until an external force again acts on this pen in space. The same thing can be attributed to the motion of this body. If the body mass is considerable, then the Law of Gravitation can exert its influence on the trajectory of this body in space.

Also whether the collision will be inelastic has to be considered along with centre of mass of the system, but you start with the basics and move forward.

A Former Brilliant Member - 3 years, 5 months ago

If you draw the free body diagram of the body, you will there is just one force acting on the body. Using F=maF = ma, where FF is the net force, and aa is the acceleration of the center of mass of the object, we see that a=Fma = \frac{F}{m}. So there will be linear motion of the center of mass. Since the torque about the center of mass is not zero, there will be some rotational motion too.

If there was another force of equal magnitude, at the same radius but in the opposite direction to the first force, then yes, there will be just rotational motion with no linear motion of the center of mass. There will be zero net force, but non-zero net torque.

Pranshu Gaba - 3 years, 4 months ago
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